tag:blogger.com,1999:blog-28967959977998320592024-02-19T08:28:35.247-08:00MATEMÁTICAS ACADÉMICAS 4º ESOTomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.comBlogger35125tag:blogger.com,1999:blog-2896795997799832059.post-54323560808679381982050-01-01T11:43:00.000-08:002020-03-19T14:19:56.285-07:00<div style="background-color: white; color: #4c1008; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; text-align: center;">
<span style="color: #20124d; font-family: "verdana" , sans-serif; font-size: large;">PRESENTACIÓN</span></div>
<span style="background-color: white; color: #20124d; font-family: "verdana" , sans-serif; font-size: 14.85px;">Hola chic@s, gracias por conectaros, espero que durante estos días podamos hacer un repaso de lo ya aprendido y avanzar un poco en la asignatura, esperando que todo vuelva a la normalidad lo más pronto posible.</span><br />
<span style="background-color: white; color: #20124d; font-family: "verdana" , sans-serif; font-size: 14.85px;">Para cualquier duda podéis enviarme un mensaje al siguiente dirección de email: <a href="https://mail.google.com/mail/?view=cm&fs=1&to=direccionpondal%40gmail.com&authuser=0" rel="nofollow" style="color: #130099; text-decoration-line: none;" target="_blank">direccionpondal@gmail.com</a></span><br />
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<span style="background-color: white; color: #20124d; font-family: "verdana" , sans-serif; font-size: 14.85px;">Cada entrada del blog se corresponde con la tarea planteada para cada día que en vuestro horario tuvieseis matemáticas y mientras dure el aislamiento iré colgando más tareas, por lo que tendréis que visitar el blog periódicamente. Las actividades planteadas tendréis que realizarlas en el cuaderno de clase así que mucho ánimo.</span><br />
<span style="background-color: white; color: #20124d; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px;"><br /></span><span style="background-color: white; color: #20124d; font-family: "verdana" , sans-serif; font-size: 14.85px;">Aquí os dejo una interesante conferencia de un gran comunicador llamado Eduardo Sáenz para aquellos que queráis visualizarla. Trata sobre las matemáticas y la educación que espero que os haga reflexionar.</span><br />
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Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-39587002508359764482020-08-09T13:44:00.004-07:002020-08-09T13:44:40.058-07:00<p> </p><p>Hola chicos, es hora de poneros ya más en serio a repasar para el curso que viene.</p><p>Adjunto el siguiente link:</p><p> <a href="https://www.matematicasonline.es/BachilleratoCCNN/Primero/mat1-Bach-ciencias8.html">https://www.matematicasonline.es/BachilleratoCCNN/Primero/mat1-Bach-ciencias8.html</a>en</p><p>En el encontraréis ejercicios de repaso para que podáis prepararos. Como veréis hay muchas partes que ya vimos este año en 4º ESO y que recomiendo que hagáis para repasar como son <a href="https://www.matematicasonline.es/BachilleratoCCNN/Primero/mat1-Bach-ciencias1.html" style="background-color: white; color: black; font-family: Arial; font-size: 16px; font-weight: 700; text-decoration-line: none;" target="_parent">Números reales, intervalos, potencias y raíces</a>, <a href="https://www.matematicasonline.es/BachilleratoCCNN/Primero/mat1-Bach-ciencias5.html" style="background-color: white; color: #990000; font-family: Arial; font-size: 16px; font-weight: 700; text-decoration-line: none;" target="_parent">Expresiones algebráicas. Polinomios</a>, <a href="https://www.matematicasonline.es/BachilleratoCCNN/Primero/mat1-Bach-ciencias6.html" style="background-color: white; color: black; font-family: Arial; font-size: 16px; font-weight: 700; text-decoration-line: none;" target="_parent">Ecuaciones e Inecuaciones</a>, <a href="https://www.matematicasonline.es/BachilleratoCCNN/Primero/mat1-Bach-ciencias7.html" style="background-color: white; color: #990000; font-family: Arial; font-size: 16px; font-weight: 700; text-decoration-line: none;" target="_parent">Sistemas de ecuaciones. Método de Gauss</a>, <a href="https://www.matematicasonline.es/BachilleratoCCNN/Primero/mat1-Bach-ciencias8.html" style="background-color: white; color: #225868; font-family: Arial; font-size: 16px; font-weight: bold; text-decoration-line: none;" target="_parent">Trigonometría</a> o vectores y rectas. Estas son las partes que necesitáis repasar y al nivel que vimos este curso. Que nadie se agobie si no le sale algún ejercicio. Yo estoy disponible en el mail para resolveros cualquier duda.</p><p>Después hay partes que las dareis nuevas en bahillerato y que ya os explicarán. Me parece además que es una web interesante que además os puede servir de ayuda de cara al curso que viene.</p><p>Mucho ánimo.</p><p><br /></p><p><br /></p><p><br /></p>Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-4417938686767795522020-07-02T15:28:00.001-07:002020-07-03T02:17:00.088-07:0003 Julio 2020<br />
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Hola chic@s, vamos a seguir repasando para prepararnos para bachillerato. Es muy importante tener dominadas ciertas herramientas de cálculo porque el año que viene vais a encontraros con conceptos nuevos pero necesitareis dominar el cálculo numérico, las ecuaciones, polinomios, etc para poder abordar la nueva materia. No se trata de que os agobiéis, simplemente de que reforcéis algunas cosas de este curso. Os iré poniendo ejercicios para que repaséis y estaré pendiente del mail para ayudaros en todo lo que pueda. Recordad que en matemáticas se saben las cosas cuando se entienden así que cualquier duda por pequeña que sea me la preguntáis porque estaré encantado de responderos.<br />
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<b><span style="color: #20124d;">Os pongo ejercicios de repaso de la primera evaluación. Tener en cuenta que primero deberéis de tener clara la teoría y para eso podéis consultar vuestro libro de texto y además os dejo unos links donde aparece teoría acompañada de ejercicios que os puede ayudar en caso de duda:</span></b><br />
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<li><b><span style="color: #20124d;">Radicales (recordad las propiedades) </span></b><a href="https://www.superprof.es/apuntes/escolar/matematicas/aritmetica/reales/radicales-2.html#tema_potencias-racionales">https://www.superprof.es/apuntes/escolar/matematicas/aritmetica/reales/radicales-2.html#tema_potencias-racionales</a></li>
<li><b><span style="color: #20124d;">Polinomios (productos notables, regla de Ruffini, simplificación ...)</span></b><a href="https://www.superprof.es/apuntes/escolar/matematicas/algebra/polinomios/">https://www.superprof.es/apuntes/escolar/matematicas/algebra/polinomios/</a></li>
<li><b><span style="color: #20124d;">Ecuaciones (de primer grado, segundo grado, ecuaciones con raíces ...)</span></b><a href="https://www.superprof.es/apuntes/escolar/matematicas/algebra/ecuaciones/">https://www.superprof.es/apuntes/escolar/matematicas/algebra/ecuaciones/</a></li>
<li><b><span style="color: #20124d;">Inecuaciones </span></b><a href="https://www.superprof.es/apuntes/escolar/matematicas/algebra/inecuaciones/">https://www.superprof.es/apuntes/escolar/matematicas/algebra/inecuaciones/</a></li>
<li><b><span style="color: #20124d;">Sistemas </span></b><a href="https://www.superprof.es/apuntes/escolar/matematicas/algebra/sistemas">https://www.superprof.es/apuntes/escolar/matematicas/algebra/sistemas</a></li>
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<br />Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-36343183722790141482020-06-16T04:52:00.001-07:002020-06-16T04:52:24.968-07:0016 JUNIO 2020<br />
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Bueno a partir de ahora voy a proponer una serie de actividades de repaso de todo el curso para aquellos que vayáis a hacer un bachillerato en el que tengáis la asignatura de matemáticas. Como siempre estaré disponible en el mail direccionpondal@gmail.com para atender a vuestras dudas.<br />
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Hoy os propongo una prueba para repasar conceptos de la 1ª Evaluación:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjU4EXGSQ1hVuIv6lKiuae-vUG0NWCNnVLWE2TfTpAq0f4aq1Si3T9rOhEyIbr8f-8HZtrpMmLYTBtMQM2OvdVgRU6BDz4f16uC8-7VODdNgNFO1xFl9vtpe1vye_6rPdAnkLfMZic08yfk/s1600/primeiro+parcial++10-11++++++++++4%25C2%25BAESO_pagenumber.001.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="842" data-original-width="595" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjU4EXGSQ1hVuIv6lKiuae-vUG0NWCNnVLWE2TfTpAq0f4aq1Si3T9rOhEyIbr8f-8HZtrpMmLYTBtMQM2OvdVgRU6BDz4f16uC8-7VODdNgNFO1xFl9vtpe1vye_6rPdAnkLfMZic08yfk/s1600/primeiro+parcial++10-11++++++++++4%25C2%25BAESO_pagenumber.001.png" /></a></div>
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<br />Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-50142505929730305922020-06-10T05:23:00.000-07:002020-06-10T05:23:57.953-07:0010 y 12 JUNIO 2020<br />
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Hola chic@s, os dejo los últimos ejercicios de probabilidad para que hagáis. Aquí finalizaremos la materia de este curso, a partir de hoy empezaremos a hacer un repaso de todo el curso. A todos aquellos que halláis decidido hacer un bachillerato en el que tengáis la asignatura de matemáticas os recomiendo que realicéis las tareas que os proponga porque el curso que viene lo agradeceréis, sería un error pensar que el año que viene tenéis tiempo suficiente para poneros al día y por lo tanto no es cuestión de agobiarse sino de ir haciendo tareas de repaso poco a poco. Trataré de poneros ejercicios con soluciones y estaré disponible en el mail para aquellos que lo necesitéis.</div>
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<h2 style="text-align: center;">
<b>Ejercicios de probabilidad: </b></h2>
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<span style="font-size: large;">1. Lanzamos dos dados y anotamos la suma de puntos de ambos dados.<br />Juan gana si la suma de puntos es 5 o menos<br />Pedro gana si la suma de puntos es 9 o más<br />Antonio gana si la suma de puntos es 6, 7 u 8<br />¿Quién tiene más probabilidad de ganar?</span></div>
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<h2 class="h2" style="color: inherit; font-family: inherit; font-size: 15.0015px; line-height: 0.977778em; margin: 0px 0px 0.977778em; padding: 0px; text-rendering: optimizelegibility;">
SOLUCIÓN</h2>
<div style="font-size: 15.0015px; margin-bottom: 1.46667em;">
1. Al sumar los puntos de dos datos obtendremos unos valores que oscilan entre 2 (1+1) y 12 (6+6).<br class="autobr" />Además debemos recordar que el nº de casos posibles es 6 x 6 = 36</div>
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Expresamos esos datos en una tabla</div>
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<img alt=" \begin{tabular}{c|c|c}
Suma & Probabilidad & Casos\\
\hline
2 & 1/36 & (1-1)\\
\hline
3 & 2/36 & (1-2) (2-1)\\
\hline
4 & 3/36 & (1-3) (2-2) (3-1) \\
\hline
5 & 4/36 & (1-4) (2-3) (3-2) (4-1)\\
\hline
6 & 5/36 & (1-5) (2-4) (3-3) (4-2) (5-1)\\
\hline
7 & 6/36 & (1-6) (2-5) (3-4) (4-3) (5-2) (6-1)\\
\hline
8 & 5/36 & (2-6) (3-5) (4-4) (5-3) (6-2)\\
\hline
9 & 4/36 & (3-6) (4-5) (5-4) (6-3) \\
\hline
10 & 3/36 & (4-6) (5-5) (6-4)\\
\hline
11 & 2/36 & (5-6) (6-5)\\
\hline
12 & 1/36 & (6-6)\\
\hline
\end{tabular}" height="320" src="https://matematicasies.com/local/cache-vignettes/L500xH320/a00dc65292ba02a1fc5ec3de1d549e29-5a77d.png?1572604197" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title=" \begin{tabular}{c|c|c}
Suma & Probabilidad & Casos\\
\hline
2 & 1/36 & (1-1)\\
\hline
3 & 2/36 & (1-2) (2-1)\\
\hline
4 & 3/36 & (1-3) (2-2) (3-1) \\
\hline
5 & 4/36 & (1-4) (2-3) (3-2) (4-1)\\
\hline
6 & 5/36 & (1-5) (2-4) (3-3) (4-2) (5-1)\\
\hline
7 & 6/36 & (1-6) (2-5) (3-4) (4-3) (5-2) (6-1)\\
\hline
8 & 5/36 & (2-6) (3-5) (4-4) (5-3) (6-2)\\
\hline
9 & 4/36 & (3-6) (4-5) (5-4) (6-3) \\
\hline
10 & 3/36 & (4-6) (5-5) (6-4)\\
\hline
11 & 2/36 & (5-6) (6-5)\\
\hline
12 & 1/36 & (6-6)\\
\hline
\end{tabular}" width="500" /></div>
<div style="font-size: 15.0015px; margin-bottom: 1.46667em;">
Sean los sucesos:<br class="autobr" />J = "gana Juan"<br class="autobr" />P = "gana Pedro"<br class="autobr" />A = "gana Antonio"</div>
<div style="font-size: 15.0015px; margin-bottom: 1.46667em;">
Entonces las probabilidades son:<br /><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> <img alt="P(J) = \frac{1}{36}+\frac{2}{36}+\frac{3}{36}+\frac{4}{36}=\frac{10}{36}" height="65" src="https://matematicasies.com/local/cache-vignettes/L287xH65/dc12d7a4bac940f24146dd00a31137f6-1944c.png?1572604197" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="P(J) = \frac{1}{36}+\frac{2}{36}+\frac{3}{36}+\frac{4}{36}=\frac{10}{36}" width="287" /><br /><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> <img alt="P(P) = \frac{4}{36}+\frac{3}{36}+\frac{2}{36}+\frac{1}{36}=\frac{10}{36}" height="65" src="https://matematicasies.com/local/cache-vignettes/L288xH65/ba896726927b7489f89e96a24d7075d7-917a0.png?1572604197" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="P(P) = \frac{4}{36}+\frac{3}{36}+\frac{2}{36}+\frac{1}{36}=\frac{10}{36}" width="288" /><br /><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> <img alt="P(A) = \frac{5}{36}+\frac{6}{36}+\frac{5}{36}=\frac{16}{36}" height="65" src="https://matematicasies.com/local/cache-vignettes/L242xH65/e90f3683313815700e18a43566cb34a3-0d32f.png?1572604197" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="P(A) = \frac{5}{36}+\frac{6}{36}+\frac{5}{36}=\frac{16}{36}" width="242" /></div>
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Antonio tiene más probabilidad de ganar</div>
<div style="font-size: 15.0015px; margin-bottom: 1.46667em;">
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<div style="color: #333333; font-weight: 400; margin: 0px auto; overflow: hidden; width: 730px;">
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<span style="font-size: large;">2. Lanzamos tres monedas. Se pide:</span></div>
<div style="margin-bottom: 1.46667em;">
<span style="font-size: large;"><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> a) probabilidad de obtener tres caras<br /><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> b) probabilidad de obtener al menos dos caras<br /><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> c) probabilidad de obtener como mucho una cara<br /><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> d) probabilidad de no obtener ninguna cara</span></div>
</div>
<div class="chapo surlignable">
<h2 class="h2" style="color: inherit; font-family: inherit; font-size: 15.0015px; line-height: 0.977778em; margin: 0px 0px 0.977778em; padding: 0px; text-rendering: optimizelegibility;">
SOLUCIÓN</h2>
<div style="font-size: 15.0015px; margin-bottom: 1.46667em;">
Al lanzar tres monedas obtenemos el siguiente Espacio Muestral compuesto por 8 sucesos elementales:<br /><img alt="E = \{CCC, \quad CC+, \quad C+C, \quad C++, \quad +CC, \quad +C+, \quad ++C, \quad+++ \}" height="41" src="https://matematicasies.com/local/cache-vignettes/L640xH41/f110a19d76c15975944163a5d7dae35a-6a841.png?1572604277" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="E = \{CCC, \quad CC+, \quad C+C, \quad C++, \quad +CC, \quad +C+, \quad ++C, \quad+++ \}" width="640" /><br class="autobr" />Sean los sucesos:<br /><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> A = "obtener tres caras"<br /><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> B = "obtener al menos dos caras"<br /><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> C = "obtener como mucho una cara"<br /><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> D = "no obtener ninguna cara"</div>
<div style="font-size: 15.0015px; margin-bottom: 1.46667em;">
Entonces las probabilidades serían:</div>
<div style="font-size: 15.0015px; margin-bottom: 1.46667em;">
<img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> <img alt="P(A) = \frac{1}{8}" height="65" src="https://matematicasies.com/local/cache-vignettes/L87xH65/d4b60506bd55eb3bd3270ff6f6a5bb54-81532.png?1572604277" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="P(A) = \frac{1}{8}" width="87" /><br /><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> <img alt="P(B) = \frac{4}{8}" height="65" src="https://matematicasies.com/local/cache-vignettes/L88xH65/9e8ca47680febd057bfc28d8a729f006-bb43c.png?1572604277" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="P(B) = \frac{4}{8}" width="88" /><br /><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> <img alt="P(C) = \frac{4}{8}" height="65" src="https://matematicasies.com/local/cache-vignettes/L88xH65/6303d1ed33458f65b52308cbfe573e56-bde80.png?1572604277" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="P(C) = \frac{4}{8}" width="88" /><br /><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> <img alt="P(D) = \frac{1}{8}" height="65" src="https://matematicasies.com/local/cache-vignettes/L88xH65/ac7140002652f407bdcf4dac66bdc24d-0d962.png?1572604277" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="P(D) = \frac{1}{8}" width="88" /></div>
<div style="font-size: 15.0015px; margin-bottom: 1.46667em;">
<br /></div>
<div style="color: #333333; font-weight: 400; margin: 0px auto; overflow: hidden; width: 730px;">
<div style="margin-bottom: 1.46667em;">
<span style="font-size: large;">3. Lanzamos tres monedas. Se pide:</span></div>
<div style="margin-bottom: 1.46667em;">
<span style="font-size: large;"><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> a) probabilidad de obtener tres caras<br /><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> b) probabilidad de obtener al menos dos caras<br /><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> c) probabilidad de obtener como mucho una cara<br /><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> d) probabilidad de no obtener ninguna cara</span></div>
</div>
<div class="chapo surlignable">
<h2 class="h2" style="color: inherit; font-family: inherit; font-size: 15.0015px; line-height: 0.977778em; margin: 0px 0px 0.977778em; padding: 0px; text-rendering: optimizelegibility;">
SOLUCIÓN</h2>
<div style="margin-bottom: 1.46667em;">
<span style="font-size: 15.0015px;">Al lanzar tres monedas obtenemos el siguiente Espacio Muestral compuesto por 8 sucesos elementales:</span><br /><span style="border-color: initial; border-image: initial; border-style: initial; font-size: 15.0015px; height: auto;"><img alt="E = \{CCC, \quad CC+, \quad C+C, \quad C++, \quad +CC, \quad +C+, \quad ++C, \quad+++ \}" height="41" src="https://matematicasies.com/local/cache-vignettes/L640xH41/f110a19d76c15975944163a5d7dae35a-6a841.png?1572604277" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="E = \{CCC, \quad CC+, \quad C+C, \quad C++, \quad +CC, \quad +C+, \quad ++C, \quad+++ \}" width="640" /></span><br class="autobr" /> Sean los sucesos:<br /><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> A = "obtener tres caras"<br /><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> B = "obtener al menos dos caras"<br /><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> C = "obtener como mucho una cara"<br /><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> D = "no obtener ninguna cara"</div>
<div style="margin-bottom: 1.46667em;">
Entonces las probabilidades serían:</div>
<div style="font-size: 15.0015px; margin-bottom: 1.46667em;">
<img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> <img alt="P(A) = \frac{1}{8}" height="65" src="https://matematicasies.com/local/cache-vignettes/L87xH65/d4b60506bd55eb3bd3270ff6f6a5bb54-81532.png?1572604277" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="P(A) = \frac{1}{8}" width="87" /><br /><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> <img alt="P(B) = \frac{4}{8}" height="65" src="https://matematicasies.com/local/cache-vignettes/L88xH65/9e8ca47680febd057bfc28d8a729f006-bb43c.png?1572604277" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="P(B) = \frac{4}{8}" width="88" /><br /><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> <img alt="P(C) = \frac{4}{8}" height="65" src="https://matematicasies.com/local/cache-vignettes/L88xH65/6303d1ed33458f65b52308cbfe573e56-bde80.png?1572604277" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="P(C) = \frac{4}{8}" width="88" /><br /><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> <img alt="P(D) = \frac{1}{8}" height="65" src="https://matematicasies.com/local/cache-vignettes/L88xH65/ac7140002652f407bdcf4dac66bdc24d-0d962.png?1572604277" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="P(D) = \frac{1}{8}" width="88" /></div>
<div style="color: #333333; font-weight: 400; margin: 0px auto; overflow: hidden; width: 730px;">
<div style="margin-bottom: 1.46667em;">
<span style="font-size: large;">4. Elegimos al azar una ficha de un juego de dominó. Calcula la probabilidad de:</span></div>
<div style="margin-bottom: 1.46667em;">
<span style="font-size: large;"><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> a) obtener el pito doble (1-1)<br /><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> b) la suma de puntos sea 7</span></div>
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<h2 class="h2" style="color: inherit; font-family: inherit; line-height: 0.977778em; margin: 0px 0px 0.977778em; padding: 0px; text-rendering: optimizelegibility;">
SOLUCIÓN</h2>
<div style="margin-bottom: 1.46667em;">
Un dominó consta de 28 fichas numeradas como en la imagen<br class="autobr" /><span class="spip_document_867 spip_documents spip_documents_center" style="background: 0px 0px; box-sizing: border-box; clear: both; display: block; margin: 1.46667em auto; max-width: 100%; text-align: center; width: 730px;"><img alt="" height="275" src="https://matematicasies.com/local/cache-vignettes/L250xH275/maties_1968-315a6.png?1572604911" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" width="250" /></span></div>
<div style="margin-bottom: 1.46667em;">
<img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> a) <img alt="\frac{1}{28}" height="65" src="https://matematicasies.com/local/cache-vignettes/L25xH65/bcd064debafc204fd69d0b7e5042905a-9798f.png?1572604911" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="\frac{1}{28}" width="25" /></div>
<div style="margin-bottom: 1.46667em;">
<img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /> b) Para que la suma de puntos sea 7 tenemos estas posibilidades:<br class="autobr" />[1-6] [2-5] y [3-4]<br class="autobr" /><img alt="\frac{3}{28} " height="65" src="https://matematicasies.com/local/cache-vignettes/L25xH65/58b2dc7898513cccdd1444cef09bc91d-88b64.png?1572604911" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="\frac{3}{28} " width="25" /></div>
<div style="margin-bottom: 1.46667em;">
<br /></div>
</div>
</div>
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Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-90733805990859195912020-06-07T15:32:00.001-07:002020-06-07T15:32:38.475-07:008 JUNIO 2020<br />
<br />
Hola chic@s, vamos a ver el último tema de este curso. Se trata del cálculo de probabilidades.<br />
<br />
<br />
Primeramente vamos a ver un poco de teoría y después un vídeo explicativo de conceptos básicos:<br />
<h1 id="experimento-aleatorio" style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 2.3em; line-height: 1.3; margin: 1em 0px; padding: 0px;">
Experimento aleatorio<a class="header-link" href="https://crdguez.github.io/2019/03/23/Probabilidad/#experimento-aleatorio" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px 0px 0px 0.2em; opacity: 0; padding: 0px; text-decoration-line: none;"><span aria-hidden="true" class="fa fa-link" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1; margin: 0px; padding: 0px; text-rendering: auto;"></span></a></h1>
<div style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; margin-bottom: 1.5em; margin-top: 1.5em; padding: 0px;">
Un <strong style="box-sizing: border-box; margin: 0px; padding: 0px;">experimento aleatorio</strong> es aquél que si se repite varias veces no está garantizado obtener siempre el mismo resultado. Es decir, no se puede determinar cuál va a ser el resultado del experimento hasta que no se realiza. En caso contrario, decimos que el experimento es <strong style="box-sizing: border-box; margin: 0px; padding: 0px;">determinista</strong></div>
<div style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; margin-bottom: 1.5em; margin-top: 1.5em; padding: 0px;">
Un experimento es aleatorio cuando depende de muchos factores y cualquier pequeña modificación de alguno implica obtener un resultado diferente.</div>
<h3 id="ejemplos" style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; line-height: 1.3; margin: 1em 0px; padding: 0px;">
Ejemplos<a class="header-link" href="https://crdguez.github.io/2019/03/23/Probabilidad/#ejemplos" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px 0px 0px 0.2em; opacity: 0; padding: 0px; text-decoration-line: none;"><span aria-hidden="true" class="fa fa-link" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1; margin: 0px; padding: 0px; text-rendering: auto;"></span></a></h3>
<ul style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; list-style-position: inside; margin: 1.5em 0px; padding: 0px 0px 0px 1em;">
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Aleatorio</strong>: Lanzar un dado y ver el resultado</li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Determinista</strong>: Calcular el tiempo que tarda en caer un objeto al suelo desde una distancia determinada</li>
</ul>
<h1 id="espacio-muestral-y-sucesos" style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 2.3em; line-height: 1.3; margin: 1em 0px; padding: 0px;">
Espacio muestral y sucesos<a class="header-link" href="https://crdguez.github.io/2019/03/23/Probabilidad/#espacio-muestral-y-sucesos" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px 0px 0px 0.2em; opacity: 0; padding: 0px; text-decoration-line: none;"><span aria-hidden="true" class="fa fa-link" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1; margin: 0px; padding: 0px; text-rendering: auto;"></span></a></h1>
<ul style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; list-style-position: inside; margin: 1.5em 0px; padding: 0px 0px 0px 1em;">
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Espacio muestral</strong>: Conjunto de los posibles resultados del experimento. Se denota: <em style="box-sizing: border-box; margin: 0px; padding: 0px;">E</em></li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Sucesos simples o elementales</strong>: Cualquiera de los elementos del espacio muestral</li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Sucesos compuestos</strong>: Sucesos formados por varios simples.</li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Suceso seguro</strong>: Suceso compuesto por los elementos del Espacio muestral. Se cumple siempre</li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Suceso imposible</strong>: Cualquier suceso que no se cumpla nunca. Se denota con el símbolo: ⌀</li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Suceso contrario</strong>: Si <em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> es un suceso, <span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>A</mi><mo accent="false">&#x00AF;</mo></mover></math>" id="MathJax-Element-1-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.757em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 18.56px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.649em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.08em, 1000.65em, 2.427em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.26em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="munderover" id="MathJax-Span-3" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.649em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.182em, 1000.54em, 4.151em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.984em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-4" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">A</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(3.505em, 1000.65em, 3.99em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.739em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-5" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.649em;"><span style="border: 0px; box-sizing: border-box; left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.984em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; font-family: STIXGeneral; font-size: 13.1219px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">⎯</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; left: 0.434em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.984em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; font-family: STIXGeneral; font-size: 13.1219px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">⎯</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; left: 0.11em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.984em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; font-family: STIXGeneral; font-size: 13.1219px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">⎯</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; left: 0.272em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.984em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; font-family: STIXGeneral; font-size: 13.1219px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">⎯</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.266em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 1.316em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.059em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>A</mi><mo accent="false">¯</mo></mover></math></span></span> es el suceso contrario. Es aquel que se cumple cuando no se cumple <em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em></li>
</ul>
<h3 id="ejemplos-1" style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; line-height: 1.3; margin: 1em 0px; padding: 0px;">
Ejemplos<a class="header-link" href="https://crdguez.github.io/2019/03/23/Probabilidad/#ejemplos-1" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px 0px 0px 0.2em; opacity: 0; padding: 0px; text-decoration-line: none;"><span aria-hidden="true" class="fa fa-link" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1; margin: 0px; padding: 0px; text-rendering: auto;"></span></a></h3>
<div style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; margin-bottom: 1.5em; margin-top: 1.5em; padding: 0px;">
Lanzamos un dado y comprobamos la cara que sale.</div>
<ul style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; list-style-position: inside; margin: 1.5em 0px; padding: 0px 0px 0px 1em;">
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Espacio muestral</strong>: <em style="box-sizing: border-box; margin: 0px; padding: 0px;">E</em> = {1, 2, 3, 4, 5, 6}</li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Sucesos simples o elementales</strong>: 1, 2, 3, 4, 5 ó 6</li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Sucesos compuestos</strong>: <em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> = {que salga par} = {2, 4, 6}</li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Suceso seguro</strong>: <em style="box-sizing: border-box; margin: 0px; padding: 0px;">E</em> = {1, 2, 3, 4, 5, 6}</li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Suceso imposible</strong>: ⌀ = {que salga mayor que 6}</li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Suceso contrario</strong>: Si <em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> = {que salga par} = {2, 4, 6}}, <span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>A</mi><mo accent="false">&#x00AF;</mo></mover><mo>=</mo><mo fence="false" stretchy="false">{</mo><mi>q</mi><mi>u</mi><mi>e</mi><mtext>&#xA0;</mtext><mi>s</mi><mi>a</mi><mi>l</mi><mi>g</mi><mi>a</mi><mtext>&#xA0;</mtext><mi>i</mi><mi>m</mi><mi>p</mi><mi>a</mi><mi>r</mi><mo fence="false" stretchy="false">}</mo><mo>=</mo><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo fence="false" stretchy="false">}</mo></math>" id="MathJax-Element-2-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-6" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 16.22em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 18.56px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 13.957em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.35em, 1013.85em, 2.912em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.53em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-7" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="munderover" id="MathJax-Span-8" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.649em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.182em, 1000.54em, 4.151em, -999.997em); left: 0.003em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.984em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-9" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">A</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(3.505em, 1000.65em, 3.99em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.739em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-10" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.649em;"><span style="border: 0px; box-sizing: border-box; left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.984em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; font-family: STIXGeneral; font-size: 13.1219px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">⎯</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; left: 0.434em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.984em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; font-family: STIXGeneral; font-size: 13.1219px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">⎯</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; left: 0.11em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.984em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; font-family: STIXGeneral; font-size: 13.1219px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">⎯</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; left: 0.272em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -3.984em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; font-family: STIXGeneral; font-size: 13.1219px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">⎯</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-11" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.326em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mo" id="MathJax-Span-12" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.326em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">{</span><span class="mi" id="MathJax-Span-13" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">q</span><span class="mi" id="MathJax-Span-14" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">u</span><span class="mi" id="MathJax-Span-15" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">e</span><span class="mtext" id="MathJax-Span-16" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"> </span><span class="mi" id="MathJax-Span-17" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">s</span><span class="mi" id="MathJax-Span-18" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">a</span><span class="mi" id="MathJax-Span-19" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">l<span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-20" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">g</span><span class="mi" id="MathJax-Span-21" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">a</span><span class="mtext" id="MathJax-Span-22" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"> </span><span class="mi" id="MathJax-Span-23" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">i</span><span class="mi" id="MathJax-Span-24" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">m</span><span class="mi" id="MathJax-Span-25" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">p</span><span class="mi" id="MathJax-Span-26" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">a</span><span class="mi" id="MathJax-Span-27" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">r<span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-28" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">}</span><span class="mo" id="MathJax-Span-29" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.326em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mo" id="MathJax-Span-30" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.326em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">{</span><span class="mn" id="MathJax-Span-31" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span><span class="mo" id="MathJax-Span-32" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">,</span><span class="mn" id="MathJax-Span-33" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.164em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">3</span><span class="mo" id="MathJax-Span-34" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">,</span><span class="mn" id="MathJax-Span-35" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.164em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">5</span><span class="mo" id="MathJax-Span-36" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">}</span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.535em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 1.566em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.309em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>A</mi><mo accent="false">¯</mo></mover><mo>=</mo><mo fence="false" stretchy="false">{</mo><mi>q</mi><mi>u</mi><mi>e</mi><mtext> </mtext><mi>s</mi><mi>a</mi><mi>l</mi><mi>g</mi><mi>a</mi><mtext> </mtext><mi>i</mi><mi>m</mi><mi>p</mi><mi>a</mi><mi>r</mi><mo fence="false" stretchy="false">}</mo><mo>=</mo><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo fence="false" stretchy="false">}</mo></math></span></span></li>
</ul>
<h1 id="operaciones-con-sucesos-y-relaciones" style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 2.3em; line-height: 1.3; margin: 1em 0px; padding: 0px;">
Operaciones con sucesos y relaciones<a class="header-link" href="https://crdguez.github.io/2019/03/23/Probabilidad/#operaciones-con-sucesos-y-relaciones" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px 0px 0px 0.2em; opacity: 0; padding: 0px; text-decoration-line: none;"><span aria-hidden="true" class="fa fa-link" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1; margin: 0px; padding: 0px; text-rendering: auto;"></span></a></h1>
<ul style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; list-style-position: inside; margin: 1.5em 0px; padding: 0px 0px 0px 1em;">
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Unión</strong>: la unión de los sucesos <em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> y <em style="box-sizing: border-box; margin: 0px; padding: 0px;">B</em> es aquel suceso que contiene a todos los elementos de <em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> y a los de <em style="box-sizing: border-box; margin: 0px; padding: 0px;">B</em>. Se denota: <em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> ∪ <em style="box-sizing: border-box; margin: 0px; padding: 0px;">B</em></li>
</ul>
<div style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; margin-bottom: 1.5em; margin-top: 1.5em; padding: 0px; text-align: center;">
<a href="https://crdguez.github.io/assets/img/tikz_union.png" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px; padding: 0px; text-decoration-line: none;" target="_blank"><img src="https://crdguez.github.io/assets/img/tikz_union.png" style="border: 0px; box-sizing: border-box; margin: 0px; max-width: 100%; padding: 0px;" width="30%" /></a></div>
<ul style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; list-style-position: inside; margin: 1.5em 0px; padding: 0px 0px 0px 1em;">
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><strong style="box-sizing: border-box; margin: 0px; padding: 0px;">Intersección</strong>: la intersección de los sucesos <em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> y <em style="box-sizing: border-box; margin: 0px; padding: 0px;">B</em> es aquel suceso que contiene a todos los elementos que están tanto en <em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> como en <em style="box-sizing: border-box; margin: 0px; padding: 0px;">B</em>. Se denota: <em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> ∩ <em style="box-sizing: border-box; margin: 0px; padding: 0px;">B</em></li>
</ul>
<div style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; margin-bottom: 1.5em; margin-top: 1.5em; padding: 0px; text-align: center;">
<a href="https://crdguez.github.io/assets/img/tikz_interseccion.png" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px; padding: 0px; text-decoration-line: none;" target="_blank"><img src="https://crdguez.github.io/assets/img/tikz_interseccion.png" style="border: 0px; box-sizing: border-box; margin: 0px; max-width: 100%; padding: 0px;" width="30%" /></a></div>
<h3 id="ejemplos-2" style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; line-height: 1.3; margin: 1em 0px; padding: 0px;">
Ejemplos<a class="header-link" href="https://crdguez.github.io/2019/03/23/Probabilidad/#ejemplos-2" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px 0px 0px 0.2em; opacity: 0; padding: 0px; text-decoration-line: none;"><span aria-hidden="true" class="fa fa-link" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1; margin: 0px; padding: 0px; text-rendering: auto;"></span></a></h3>
<div style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; margin-bottom: 1.5em; margin-top: 1.5em; padding: 0px;">
Tomamos como experimento el resultado de lanzar un dado, y los sucesos:</div>
<table style="background-color: white; border-collapse: collapse; border-spacing: 0px; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; margin: 1.5em 0px; padding: 0px; width: 840px;"><tbody style="box-sizing: border-box; margin: 0px; padding: 0px;">
<tr class="odd" style="box-sizing: border-box; margin: 0px; padding: 0px;"><td style="border: 1px solid rgba(0, 0, 0, 0.1); box-sizing: border-box; margin: 0px; padding: 0.5em 1em;"><span class="math inline" style="box-sizing: border-box; margin: 0px; padding: 0px;"><em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> = {<em style="box-sizing: border-box; margin: 0px; padding: 0px;">q</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">u</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">e</em> <em style="box-sizing: border-box; margin: 0px; padding: 0px;">s</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">a</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">l</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">g</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">a</em> <em style="box-sizing: border-box; margin: 0px; padding: 0px;">p</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">a</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">r</em>} = {2, 4, 6}</span></td></tr>
<tr class="even" style="box-sizing: border-box; margin: 0px; padding: 0px;"><td style="border: 1px solid rgba(0, 0, 0, 0.1); box-sizing: border-box; margin: 0px; padding: 0.5em 1em;"><span class="math inline" style="box-sizing: border-box; margin: 0px; padding: 0px;"><em style="box-sizing: border-box; margin: 0px; padding: 0px;">B</em> = {<em style="box-sizing: border-box; margin: 0px; padding: 0px;">q</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">u</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">e</em> <em style="box-sizing: border-box; margin: 0px; padding: 0px;">s</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">e</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">a</em> <em style="box-sizing: border-box; margin: 0px; padding: 0px;">m</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">a</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">y</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">o</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">r</em> <em style="box-sizing: border-box; margin: 0px; padding: 0px;">q</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">u</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">e</em> 3} = {4, 5, 6}</span></td></tr>
<tr class="odd" style="box-sizing: border-box; margin: 0px; padding: 0px;"><td style="border: 1px solid rgba(0, 0, 0, 0.1); box-sizing: border-box; margin: 0px; padding: 0.5em 1em;"><span class="math inline" style="box-sizing: border-box; margin: 0px; padding: 0px;"><em style="box-sizing: border-box; margin: 0px; padding: 0px;">C</em> = {<em style="box-sizing: border-box; margin: 0px; padding: 0px;">q</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">u</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">e</em> <em style="box-sizing: border-box; margin: 0px; padding: 0px;">s</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">a</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">l</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">g</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">a</em> <em style="box-sizing: border-box; margin: 0px; padding: 0px;">i</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">m</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">p</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">a</em><em style="box-sizing: border-box; margin: 0px; padding: 0px;">r</em>} = {1, 3, 5}</span></td></tr>
</tbody></table>
<ul style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; list-style-position: inside; margin: 1.5em 0px; padding: 0px 0px 0px 1em;">
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> ∪ <em style="box-sizing: border-box; margin: 0px; padding: 0px;">B</em> = {2, 4, 5, 6}<br style="box-sizing: border-box; margin: 0px; padding: 0px;" /><a href="https://crdguez.github.io/assets/img/tikz_ej_union.png" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px; padding: 0px; text-decoration-line: none;" target="_blank"><img src="https://crdguez.github.io/assets/img/tikz_ej_union.png" style="border: 0px; box-sizing: border-box; margin: 0px; max-width: 100%; padding: 0px;" width="30%" /></a></li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> ∩ <em style="box-sizing: border-box; margin: 0px; padding: 0px;">B</em> = {4, 6}<br style="box-sizing: border-box; margin: 0px; padding: 0px;" /><a href="https://crdguez.github.io/assets/img/tikz_ej_interseccion.png" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px; padding: 0px; text-decoration-line: none;" target="_blank"><img src="https://crdguez.github.io/assets/img/tikz_ej_interseccion.png" style="border: 0px; box-sizing: border-box; margin: 0px; max-width: 100%; padding: 0px;" width="30%" /></a></li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> ∪ <em style="box-sizing: border-box; margin: 0px; padding: 0px;">C</em> = {1, 2, 3, 4, 5, 6} = <em style="box-sizing: border-box; margin: 0px; padding: 0px;">E</em></li>
<li style="box-sizing: border-box; margin: 0px; padding: 0px;"><em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> ∩ <em style="box-sizing: border-box; margin: 0px; padding: 0px;">C</em> = ⌀</li>
</ul>
<h2 id="compatibilidad-de-sucesos" style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 1.9em; line-height: 1.3; margin: 1em 0px; padding: 0px;">
Compatibilidad de sucesos<a class="header-link" href="https://crdguez.github.io/2019/03/23/Probabilidad/#compatibilidad-de-sucesos" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px 0px 0px 0.2em; opacity: 0; padding: 0px; text-decoration-line: none;"><span aria-hidden="true" class="fa fa-link" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1; margin: 0px; padding: 0px; text-rendering: auto;"></span></a></h2>
<div style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; margin-bottom: 1.5em; margin-top: 1.5em; padding: 0px;">
Se dice que dos sucesos son incompatibles cuando su intersección es el conjunto vacío. En caso contrario se dice que son compatibles.</div>
<h3 id="ejemplo" style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; line-height: 1.3; margin: 1em 0px; padding: 0px;">
Ejemplo<a class="header-link" href="https://crdguez.github.io/2019/03/23/Probabilidad/#ejemplo" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px 0px 0px 0.2em; opacity: 0; padding: 0px; text-decoration-line: none;"><span aria-hidden="true" class="fa fa-link" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1; margin: 0px; padding: 0px; text-rendering: auto;"></span></a></h3>
<div style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; margin-bottom: 1.5em; margin-top: 1.5em; padding: 0px;">
En el ejemplo anterior, <em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> y <em style="box-sizing: border-box; margin: 0px; padding: 0px;">B</em> son compatibles y <em style="box-sizing: border-box; margin: 0px; padding: 0px;">A</em> y <em style="box-sizing: border-box; margin: 0px; padding: 0px;">C</em> incompatibles.</div>
<h1 id="probabilidad-en-experimentos-regulares-y-regla-de-laplace" style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 2.3em; line-height: 1.3; margin: 1em 0px; padding: 0px;">
Probabilidad en experimentos regulares y Regla de Laplace<a class="header-link" href="https://crdguez.github.io/2019/03/23/Probabilidad/#probabilidad-en-experimentos-regulares-y-regla-de-laplace" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px 0px 0px 0.2em; opacity: 0; padding: 0px; text-decoration-line: none;"><span aria-hidden="true" class="fa fa-link" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1; margin: 0px; padding: 0px; text-rendering: auto;"></span></a></h1>
<div style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; line-height: 1.5; margin-bottom: 1.5em; margin-top: 1.5em; padding: 0px;">
Cuando todos los sucesos elementales de un <strong style="box-sizing: border-box; margin: 0px; padding: 0px;">espacio muestral finito</strong> están en las mismas condiciones de suceder se dice que son <strong style="box-sizing: border-box; margin: 0px; padding: 0px;">equiprobables</strong>, y al experimento se le llama <strong style="box-sizing: border-box; margin: 0px; padding: 0px;">regular</strong>.</div>
<h3 id="ejemplos-de-experimentos-regulares" style="background-color: white; box-sizing: border-box; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; line-height: 1.3; margin: 1em 0px; padding: 0px;">
Ejemplos de experimentos regulares<a class="header-link" href="https://crdguez.github.io/2019/03/23/Probabilidad/#ejemplos-de-experimentos-regulares" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px 0px 0px 0.2em; opacity: 0; padding: 0px; text-decoration-line: none;"><span aria-hidden="true" class="fa fa-link" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1; margin: 0px; padding: 0px; text-rendering: auto;"></span></a></h3>
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Lanzamiento de dados, monedas, extracción de cartas, …</div>
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Regla de Laplace<a class="header-link" href="https://crdguez.github.io/2019/03/23/Probabilidad/#regla-de-laplace" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px 0px 0px 0.2em; opacity: 0; padding: 0px; text-decoration-line: none;"><span aria-hidden="true" class="fa fa-link" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1; margin: 0px; padding: 0px; text-rendering: auto;"></span></a></h2>
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La probabilidad de un suceso de un experimento regular viene determinada por la Regla de Laplace:</div>
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line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-37" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 12.341em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 18.56px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 10.617em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.026em, 1010.62em, 3.613em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.53em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-38" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-39" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">P</span><span class="mo" id="MathJax-Span-40" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">(</span><span class="mi" id="MathJax-Span-41" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">A</span><span class="mo" id="MathJax-Span-42" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">)</span><span class="mo" id="MathJax-Span-43" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.326em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mstyle" id="MathJax-Span-44" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.326em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-45" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-46" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.11em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 7.223em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1007.12em, 4.367em, -999.997em); left: 67.0156px; line-height: normal; margin: 0px 0px 0px -3.553em; padding: 0px; position: absolute; top: -4.685em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-47" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-48" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">C<span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-49" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">a</span><span class="mi" id="MathJax-Span-50" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">s</span><span class="mi" id="MathJax-Span-51" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; 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padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.164em;"></span></span><span class="mi" id="MathJax-Span-55" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">a</span><span class="mi" id="MathJax-Span-56" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">v</span><span class="mi" id="MathJax-Span-57" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">o</span><span class="mi" id="MathJax-Span-58" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">r<span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-59" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">a</span><span class="mi" id="MathJax-Span-60" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">b</span><span class="mi" id="MathJax-Span-61" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">l<span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-62" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">e</span><span class="mi" id="MathJax-Span-63" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">s</span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1005.98em, 4.367em, -999.997em); left: 67.0156px; line-height: normal; margin: 0px 0px 0px -3.015em; padding: 0px; position: absolute; top: -3.284em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-64" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-65" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">C<span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-66" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">a</span><span class="mi" id="MathJax-Span-67" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">s</span><span class="mi" id="MathJax-Span-68" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">o</span><span class="mi" id="MathJax-Span-69" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">s</span><span class="mtext" id="MathJax-Span-70" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"> </span><span class="mi" id="MathJax-Span-71" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">p</span><span class="mi" id="MathJax-Span-72" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">o</span><span class="mi" id="MathJax-Span-73" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">s</span><span class="mi" id="MathJax-Span-74" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">i</span><span class="mi" id="MathJax-Span-75" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">b</span><span class="mi" id="MathJax-Span-76" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">l<span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-77" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">e</span><span class="mi" id="MathJax-Span-78" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; font-style: italic; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">s</span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(0.865em, 1007.22em, 1.242em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.29em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 7.223em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.08em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.535em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 2.753em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -1.122em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>o</mi><mi>s</mi><mtext> </mtext><mi>f</mi><mi>a</mi><mi>v</mi><mi>o</mi><mi>r</mi><mi>a</mi><mi>b</mi><mi>l</mi><mi>e</mi><mi>s</mi></mrow><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>o</mi><mi>s</mi><mtext> </mtext><mi>p</mi><mi>o</mi><mi>s</mi><mi>i</mi><mi>b</mi><mi>l</mi><mi>e</mi><mi>s</mi></mrow></mfrac></mstyle></math></span></span></div>
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Ejemplo<a class="header-link" href="https://crdguez.github.io/2019/03/23/Probabilidad/#ejemplo-1" style="background-color: transparent; box-sizing: border-box; color: #154c68; margin: 0px 0px 0px 0.2em; opacity: 0; padding: 0px; text-decoration-line: none;"><span aria-hidden="true" class="fa fa-link" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1; margin: 0px; padding: 0px; text-rendering: auto;"></span></a></h3>
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Al lanzar un dado, los casos posibles son 6 ({1, 2, 3, 4, 5, 6}):</div>
<table style="background-color: white; border-collapse: collapse; border-spacing: 0px; color: #383838; font-family: "Source Sans Pro", Helvetica, Arial, sans-serif; font-size: 16px; margin: 1.5em 0px; padding: 0px; width: 840px;"><tbody style="box-sizing: border-box; margin: 0px; padding: 0px;">
<tr class="odd" style="box-sizing: border-box; margin: 0px; padding: 0px;"><td style="border: 1px solid rgba(0, 0, 0, 0.1); box-sizing: border-box; margin: 0px; padding: 0.5em 1em;">La probabilidad de sacar un 3: <span class="math inline" style="box-sizing: border-box; margin: 0px; padding: 0px;"><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>3</mn><mo fence="false" stretchy="false">}</mo><mo stretchy="false">&#x2192;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>6</mn></mfrac></mstyle></math>" id="MathJax-Element-4-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-79" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 4.529em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 18.56px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.882em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.026em, 1003.88em, 3.397em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.53em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-80" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-81" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">{</span><span class="mn" id="MathJax-Span-82" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">3</span><span class="mo" id="MathJax-Span-83" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">}</span><span class="mo" id="MathJax-Span-84" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.326em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">→</span><span class="mstyle" id="MathJax-Span-85" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.326em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-86" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-87" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.11em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.649em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1000.38em, 4.151em, -999.997em); left: 6.01563px; line-height: normal; margin: 0px 0px 0px -0.267em; padding: 0px; position: absolute; top: -4.685em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-88" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1000.49em, 4.151em, -999.997em); left: 6.01563px; line-height: normal; margin: 0px 0px 0px -0.267em; padding: 0px; position: absolute; top: -3.284em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-89" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">6</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(0.865em, 1000.65em, 1.242em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.29em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 0.649em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.08em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.535em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 2.503em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.872em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>3</mn><mo fence="false" stretchy="false">}</mo><mo stretchy="false">→</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>6</mn></mfrac></mstyle></math></span></span></span></td></tr>
<tr class="even" style="box-sizing: border-box; margin: 0px; padding: 0px;"><td style="border: 1px solid rgba(0, 0, 0, 0.1); box-sizing: border-box; margin: 0px; padding: 0.5em 1em;">La probabilidad de sacar par: <span class="math inline" style="box-sizing: border-box; margin: 0px; padding: 0px;"><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo fence="false" stretchy="false">}</mo><mo stretchy="false">&#x2192;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>3</mn><mn>6</mn></mfrac></mstyle></math>" id="MathJax-Element-5-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-90" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 6.63em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 18.56px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 5.714em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.026em, 1005.71em, 3.397em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.53em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-91" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-92" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">{</span><span class="mn" id="MathJax-Span-93" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span class="mo" id="MathJax-Span-94" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">,</span><span class="mn" id="MathJax-Span-95" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.164em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">4</span><span class="mo" id="MathJax-Span-96" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">,</span><span class="mn" id="MathJax-Span-97" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.164em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">6</span><span class="mo" id="MathJax-Span-98" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">}</span><span class="mo" id="MathJax-Span-99" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.326em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">→</span><span class="mstyle" id="MathJax-Span-100" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.326em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-101" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-102" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.11em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.649em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1000.43em, 4.151em, -999.997em); left: 6.01563px; line-height: normal; margin: 0px 0px 0px -0.267em; padding: 0px; position: absolute; top: -4.685em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-103" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">3</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1000.49em, 4.151em, -999.997em); left: 6.01563px; line-height: normal; margin: 0px 0px 0px -0.267em; padding: 0px; position: absolute; top: -3.284em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-104" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">6</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(0.865em, 1000.65em, 1.242em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.29em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 0.649em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.08em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.535em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 2.503em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.872em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo fence="false" stretchy="false">}</mo><mo stretchy="false">→</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>3</mn><mn>6</mn></mfrac></mstyle></math></span></span></span></td></tr>
<tr class="odd" style="box-sizing: border-box; margin: 0px; padding: 0px;"><td style="border: 1px solid rgba(0, 0, 0, 0.1); box-sizing: border-box; margin: 0px; padding: 0.5em 1em;">La probabilidad de sacar más de 4: <span class="math inline" style="box-sizing: border-box; margin: 0px; padding: 0px;"><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo fence="false" stretchy="false">}</mo><mo stretchy="false">&#x2192;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>2</mn><mn>6</mn></mfrac></mstyle></math>" id="MathJax-Element-6-Frame" role="presentation" style="border: 0px; box-sizing: border-box; direction: ltr; display: inline; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; box-sizing: border-box; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-105" style="border: 0px; box-sizing: border-box; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 5.606em;"><span style="border: 0px; box-sizing: border-box; display: inline-block; font-size: 18.56px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 4.798em;"><span style="border: 0px; box-sizing: border-box; clip: rect(1.026em, 1004.8em, 3.397em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.53em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-106" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-107" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">{</span><span class="mn" id="MathJax-Span-108" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">5</span><span class="mo" id="MathJax-Span-109" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">,</span><span class="mn" id="MathJax-Span-110" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.164em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">6</span><span class="mo" id="MathJax-Span-111" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">}</span><span class="mo" id="MathJax-Span-112" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.326em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">→</span><span class="mstyle" id="MathJax-Span-113" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.326em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-114" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-115" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.11em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.649em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1000.49em, 4.151em, -999.997em); left: 6.01563px; line-height: normal; margin: 0px 0px 0px -0.267em; padding: 0px; position: absolute; top: -4.685em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-116" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(3.128em, 1000.49em, 4.151em, -999.997em); left: 6.01563px; line-height: normal; margin: 0px 0px 0px -0.267em; padding: 0px; position: absolute; top: -3.284em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-117" style="border: 0px; box-sizing: border-box; display: inline; font-family: STIXGeneral; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">6</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 3.99em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: border-box; clip: rect(0.865em, 1000.65em, 1.242em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.29em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; box-sizing: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 0.649em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.08em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.535em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: border-box; display: inline-block; height: 2.503em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.872em; width: 0px;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; box-sizing: border-box; clip: rect(1px, 1px, 1px, 1px); display: inline; height: 1px !important; left: 0px; line-height: normal; margin: 0px; overflow: hidden !important; padding: 0px; position: static; top: 0px; transition: none 0s ease 0s; user-select: none; vertical-align: 0px; width: 1px !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">{</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo fence="false" stretchy="false">}</mo><mo stretchy="false">→</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>2</mn><mn>6</mn></mfrac></mstyle></math></span></span></span></td></tr>
</tbody></table>
<div style="background-color: white; box-sizing: border-box; color: #383838; line-height: 1.3; margin: 1em 0px; padding: 0px;">
<span style="font-family: Verdana, sans-serif;">Os dejo un vídeo explicativo:</span></div>
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<iframe width="320" height="266" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/2XWejSaiwNE/0.jpg" src="https://www.youtube.com/embed/2XWejSaiwNE?feature=player_embedded" frameborder="0" allowfullscreen></iframe></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
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<span style="font-family: Verdana, sans-serif;"><br /></span></div>
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<span style="font-family: Verdana, sans-serif;">A continuación dejo tres ejercicios con soluciones para que comprobéis si lo habléis entendido bien:</span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-family: Verdana, sans-serif;"><br /></span></div>
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<span style="font-family: Verdana, sans-serif;"><br /></span></div>
<div style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px; text-align: left;">
<span style="font-family: Verdana, sans-serif;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">1</span> Hallar la probabilidad de que al lanzar dos monedas al aire salgan dos caras.</span></div>
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<span style="background-color: #fff4f6; color: #fa6484; font-style: inherit; font-variant-caps: inherit; font-variant-ligatures: inherit; font-weight: 600;"><span style="font-family: Verdana, sans-serif;">Solución</span></span></div>
<div class="vea" style="background: url("../../../../../../../../../themes/sp_ressources_es/assets/img/solucion-white.svg") left 8px top 8px no-repeat rgb(255, 244, 246); border-radius: 5px; box-sizing: inherit; color: #222222; margin: 4rem 0px; padding: 0.5rem 1rem 0.5rem 4rem; width: auto;">
<div class="solution visible" style="background-repeat: no-repeat; box-sizing: inherit; margin: 0px; padding: 0px;">
<div style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px;">
<br /></div>
<section style="background-repeat: no-repeat; box-sizing: inherit; margin: 0px; padding: 0px;"><div class="b" style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; margin-left: 4rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;"><span style="background-repeat: no-repeat; box-sizing: inherit; font-weight: bolder; margin: 0px; padding: 0px;">Casos posibles:</span> <img alt="{cc, cx, xc, xx}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-6597679b04056c75ae251608526874e4_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -4px;" title="Rendered by QuickLaTeX.com" />.</span></div>
<div class="b" style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; margin-left: 4rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;"><span style="background-repeat: no-repeat; box-sizing: inherit; font-weight: bolder; margin: 0px; padding: 0px;">Casos favorables:</span> <img alt="1" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-db3f284c3a29040018db4577da2b7c9d_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -1px;" title="Rendered by QuickLaTeX.com" />.</span></div>
<div style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;">Aplicando la Ley de Laplace la probabilidad de que salgan dos caras es:</span></div>
<div class="b" style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; margin-left: 4rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;"><img alt="\displaystyle \text{P(2 caras)}=\frac{1}{4}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-53a5983f322357750e1ab8cf27765ac2_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -15px;" title="Rendered by QuickLaTeX.com" /></span></div>
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<br /></div>
</section></div>
</div>
<div style="background-repeat: no-repeat; box-sizing: inherit; color: #222222; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px; text-align: left;">
<span style="font-family: Verdana, sans-serif;"><span style="background-color: #f7f7f7;"><b>2</b></span><span style="background-color: white;"> Calcular la probabilidad de que al echar un dado al aire, salga:</span></span></div>
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</div>
<ul style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; line-height: 3.37rem; list-style-image: initial; list-style-position: initial; margin: 0px 0px 0px 20px; padding: 0px;">
<li style="background-repeat: no-repeat; box-sizing: inherit; line-height: 3.37rem; list-style: disc; margin: 0px 0px 0px 20px; padding: 0px;"><span style="font-family: Verdana, sans-serif;">Un número par</span></li>
</ul>
<ul style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; line-height: 3.37rem; list-style-image: initial; list-style-position: initial; margin: 0px 0px 0px 20px; padding: 0px;">
<li style="background-repeat: no-repeat; box-sizing: inherit; line-height: 3.37rem; list-style: disc; margin: 0px 0px 0px 20px; padding: 0px;"><span style="font-family: Verdana, sans-serif;">Un múltiplo de tres</span></li>
</ul>
<ul style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; line-height: 3.37rem; list-style-image: initial; list-style-position: initial; margin: 0px 0px 0px 20px; padding: 0px;">
<li style="background-repeat: no-repeat; box-sizing: inherit; line-height: 3.37rem; list-style: disc; margin: 0px 0px 0px 20px; padding: 0px;"><span style="font-family: Verdana, sans-serif;">Un número mayor que <img alt="4" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-9b5cb7cb1ca094bcfb9bce4832407b71_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -1px;" title="Rendered by QuickLaTeX.com" /></span></li>
</ul>
<span style="font-family: Verdana, sans-serif;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;"></span><span class="sa" style="background: rgb(34, 34, 34); border-radius: 50%; box-sizing: inherit; color: #f7f7f7; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">1</span> <span style="background-repeat: no-repeat; box-sizing: inherit; font-weight: bolder; margin: 0px; padding: 0px;">Un número par.</span></span><br />
<div style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;"></span></span></div>
<div class="vea" style="background: url("../../../../../../../../../themes/sp_ressources_es/assets/img/solucion-white.svg") left 8px top 8px no-repeat rgb(255, 244, 246); border-radius: 5px; box-sizing: inherit; color: #222222; margin: 4rem 0px; padding: 0.5rem 1rem 0.5rem 4rem; width: auto;">
<div style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px;">
<button class="loaded active" data-prev_post_id="14624" data-prev_post_url="https://www.superprof.es/apuntes/escolar/matematicas/algebra/ecuaciones/ecuaciones-racionales-2.html" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; color: #fa6484; cursor: pointer; display: block; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: 600; line-height: inherit; margin: 0px; overflow: visible; padding: 0px; position: relative; text-align: left; width: 650px;" type="button"><span style="font-family: Verdana, sans-serif; font-size: small;">Solución</span></button></div>
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<section style="background-repeat: no-repeat; box-sizing: inherit; margin: 0px; padding: 0px;"><div style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px;">
</div>
<div class="b" style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; margin-left: 4rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;">Casos posibles: <img alt="{1, 2, 3, 4, 5, 6}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-a916fb7c8663184066d51ba624c6e662_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -4px;" title="Rendered by QuickLaTeX.com" />.</span></div>
<div class="b" style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; margin-left: 4rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;">Casos favorables: <span class="b" style="background-repeat: no-repeat; box-sizing: inherit; margin: 0px; padding: 0px;"><img alt="{2, 4, 6}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-9ff9ff41a4e0c80e8a6191d4014d2b4b_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -4px;" title="Rendered by QuickLaTeX.com" />.</span></span></div>
<div style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;">Aplicando la Ley de Laplace la probabilidad es:</span></div>
<div class="b" style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; margin-left: 4rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;"><img alt="\displaystyle \text{P(par)}=\frac{3}{6}=\frac{1}{2}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-e8b6d007497da964b07985efd698dbb6_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -14px;" title="Rendered by QuickLaTeX.com" /></span></div>
<div style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;"><span class="sa" style="background: rgb(34, 34, 34); border-radius: 50%; box-sizing: inherit; color: #f7f7f7; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">2</span> <span style="background-repeat: no-repeat; box-sizing: inherit; font-weight: bolder; margin: 0px; padding: 0px;">Un múltiplo de tres.</span></span></div>
<div class="b" style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; margin-left: 4rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;">Casos posibles: <img alt="{1, 2, 3, 4, 5, 6}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-a916fb7c8663184066d51ba624c6e662_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -4px;" title="Rendered by QuickLaTeX.com" />.</span></div>
<div class="b" style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; margin-left: 4rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;">Casos favorables: <span class="b" style="background-repeat: no-repeat; box-sizing: inherit; margin: 0px; padding: 0px;"><img alt="{3, 6}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-bf4c00e769ee3c6d985d2bb4dd095833_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -4px;" title="Rendered by QuickLaTeX.com" />.</span></span></div>
<div style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;">Aplicando la Ley de Laplace la probabilidad es:</span></div>
<div class="b" style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; margin-left: 4rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;"><img alt="\displaystyle \text{P(multiplo de 3)}=\frac{2}{6}=\frac{1}{3}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-531e43cfcec613ccaca7decdd2802c59_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -14px;" title="Rendered by QuickLaTeX.com" /></span></div>
<div style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;"><span class="sa" style="background: rgb(34, 34, 34); border-radius: 50%; box-sizing: inherit; color: #f7f7f7; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">3</span> <span style="background-repeat: no-repeat; box-sizing: inherit; font-weight: bolder; margin: 0px; padding: 0px;">Mayor que 4.</span></span></div>
<div class="b" style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; margin-left: 4rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;">Casos posibles: <img alt="{1, 2, 3, 4, 5, 6}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-a916fb7c8663184066d51ba624c6e662_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -4px;" title="Rendered by QuickLaTeX.com" /></span></div>
<div class="b" style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; margin-left: 4rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;">Casos favorables: <span class="b" style="background-repeat: no-repeat; box-sizing: inherit; margin: 0px; padding: 0px;"><img alt="{5, 6}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-7de4038dd87035d4060ca5ffdc7aecec_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -4px;" title="Rendered by QuickLaTeX.com" />.</span></span></div>
<div style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;">Aplicando la Ley de Laplace la probabilidad es:</span></div>
<div class="b" style="background-repeat: no-repeat; box-sizing: inherit; hyphens: none; line-height: 3rem; margin-bottom: 1rem; margin-left: 4rem; padding: 0px;">
<span style="font-family: Verdana, sans-serif;"><img alt="\displaystyle \text{P(mayor que 4)}=\frac{2}{6}=\frac{1}{3}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-ca73e441dc36c70c7c88f134f1437251_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -14px;" title="Rendered by QuickLaTeX.com" /></span></div>
</section></div>
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<span style="font-family: Verdana, sans-serif;"><span style="background-color: #f7f7f7;"><b>3</b></span><span style="background-color: white;"> En una baraja de <span style="background-attachment: initial !important; background-clip: initial !important; background-image: none !important; background-origin: initial !important; background-position: initial !important; background-repeat: initial !important; background-size: initial !important; border-color: initial !important; border-image: initial !important; border-width: initial !important; box-sizing: inherit; height: auto;"><img alt="40" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-1f298b8d7c87797c5b2f1a0a4122de01_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -1px;" title="Rendered by QuickLaTeX.com" /></span> cartas, hallar la <span style="background-attachment: initial !important; background-clip: initial !important; background-image: none !important; background-origin: initial !important; background-position: initial !important; background-repeat: initial !important; background-size: initial !important; border-color: initial !important; border-image: initial !important; border-width: initial !important; box-sizing: inherit; height: auto;"><img alt="P(as)" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-c14fc987e5657d96a6d28f75cc360c4d_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -6px;" title="Rendered by QuickLaTeX.com" /></span> y <span style="background-attachment: initial !important; background-clip: initial !important; background-image: none !important; background-origin: initial !important; background-position: initial !important; background-repeat: initial !important; background-size: initial !important; border-color: initial !important; border-image: initial !important; border-width: initial !important; box-sizing: inherit; height: auto;"><img alt="P(copas)" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-6a920a16a0da3d10d8dbbdb39e7f97ef_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -6px;" title="Rendered by QuickLaTeX.com" /></span>.</span></span></div>
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<button class="loaded active" data-prev_post_id="14624" data-prev_post_url="https://www.superprof.es/apuntes/escolar/matematicas/algebra/ecuaciones/ecuaciones-racionales-2.html" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; color: #fa6484; cursor: pointer; display: block; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: 600; line-height: inherit; margin: 0px; overflow: visible; padding: 0px; position: relative; text-align: left; width: 650px;" type="button"><span style="font-family: Verdana, sans-serif; font-size: small;">Solución</span></button></div>
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<section style="background-repeat: no-repeat; box-sizing: inherit; margin: 0px; padding: 0px;"><span style="font-family: Verdana, sans-serif;"><span class="sa" style="background: rgb(34, 34, 34); border-radius: 50%; box-sizing: inherit; color: #f7f7f7; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">1</span><span style="background-repeat: no-repeat; box-sizing: inherit; font-weight: bolder; margin: 0px; padding: 0px;">Probabilidad de obtener ases</span></span><br />
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<span style="font-family: Verdana, sans-serif;">Casos posibles: <img alt="40" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-1f298b8d7c87797c5b2f1a0a4122de01_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -1px;" title="Rendered by QuickLaTeX.com" />.</span></div>
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<span style="font-family: Verdana, sans-serif;">Casos favorables de ases: <img alt="4" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-9b5cb7cb1ca094bcfb9bce4832407b71_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -1px;" title="Rendered by QuickLaTeX.com" />.</span></div>
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<span style="font-family: Verdana, sans-serif;">Aplicando la Ley de Laplace la probabilidad de sacar un as es:</span></div>
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<span style="font-family: Verdana, sans-serif;"><img alt="\displaystyle \text{P(as)}=\frac{4}{40}=\frac{1}{10}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-eea93713c93da72ec605baaba4f8dbec_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -15px;" title="Rendered by QuickLaTeX.com" /></span></div>
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<span style="font-family: Verdana, sans-serif;"><span class="sa" style="background: rgb(34, 34, 34); border-radius: 50%; box-sizing: inherit; color: #f7f7f7; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">2</span><span style="background-repeat: no-repeat; box-sizing: inherit; font-weight: bolder; margin: 0px; padding: 0px;">Probabilidad de obtener copas</span></span></div>
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<span style="font-family: Verdana, sans-serif;">Casos posibles: <img alt="40" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-1f298b8d7c87797c5b2f1a0a4122de01_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -1px;" title="Rendered by QuickLaTeX.com" />.</span></div>
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<span style="font-family: Verdana, sans-serif;">Casos favorables de copas: <img alt="10" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-ddc4c36c7503a5b91c38e759f1714bcc_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -1px;" title="Rendered by QuickLaTeX.com" />.</span></div>
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<span style="font-family: Verdana, sans-serif;">Aplicando la Ley de Laplace la probabilidad de sacar una copa es:</span></div>
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<span style="font-family: Verdana, sans-serif;"><span style="background-attachment: initial !important; background-clip: initial !important; background-image: none !important; background-origin: initial !important; background-position: initial !important; background-repeat: initial !important; background-size: initial !important; border-color: initial !important; border-image: initial !important; border-width: initial !important; box-sizing: inherit; height: auto;"><img alt="\displaystyle \text{P(copas)}=\frac{10}{40}=\frac{1}{4}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-9ce08224ba87fb2a21938cb1e79f6789_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -15px;" title="Rendered by QuickLaTeX.com" /></span> </span></div>
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Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-17221676455642360672020-06-04T15:07:00.004-07:002020-06-04T15:09:45.196-07:005 JUNIO 2020<br />
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Hola chic@s, vamos a ver hoy la representación de funciones. En 4º de la ESO solo estamos en condiciones de representar funciones lineales y funciones cuadráticas, pero los que hagáis un bachillerato que tenga matemáticas deberéis de saber representar cualquier tipo de función. Para ello es necesario el uso de herramientas de cálculo matemático como son los límites de funciones y el concepto de derivada que veréis el año que viene que os permitirán conocer el comportamiento de la función: crecimiento y decrecimiento, concavidad y convexidad, máximos, mínimos, puntos de inflexión, asíntotas ... para poder representarlas.</div>
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Lo que quiero que veáis son ciertas gráficas de funciones asociadas a sus funciones analíticas y para ello lo vamos a hacer a través de una aplicación ya que no podemos hacerlo de otra manera. Existen muchas aplicaciones para ello, yo os dejo el link de una de ellas:</div>
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<a href="https://www.geogebra.org/graphing?lang=es">https://www.geogebra.org/graphing?lang=es</a></div>
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En la parte inferior aparece una calculadora para poner la expresión de la función que queráis representar y automáticamente aparece la gráfica. </div>
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Lo que quiero es que representéis a través de la aplicación las siguientes funciones:</div>
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a) <img alt=" \displaystyle f(x)=3x-x^3 " src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-3bacd7bea8b50ea769f43e59f6e93234_l3.png" /></div>
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b) <img alt="\displaystyle f(x)=x^4 -2x^2 -8 " src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-2353765f0a46aa54bfe95e39167309c3_l3.png" /></div>
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c) <img alt="\displaystyle f(x)= \frac{x^3}{(x-1)^2} " src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-2fcc798ad35577a1b81ee55d72fa5030_l3.png" /></div>
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d) <img alt="\displaystyle f(x) = \frac{x^2-3x+2}{x^2+1} " src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-f84b71d0bb3bf1dd1b78d3602e548124_l3.png" /><br />
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e) <img alt=" \displaystyle f(x) =(x-1)e^{-x} " src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-4864689e4a1aa96a3d54a93268dcf3c8_l3.png" /></div>
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f) <img alt="\displaystyle f(x)= \frac{\ln x}{x} " src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-182f33e1db332fee901e4865355b4bba_l3.png" /></div>
Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-79991856867199068472020-06-02T16:38:00.001-07:002020-06-03T04:23:22.549-07:003 JUNIO 2020<br />
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Buenos días chicos, entramos en la recta final del curso, vamos a ir terminando con el tema de funciones y finalmente veremos algo de probabilidad.<br />
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Vamos a recordar como se representan dos de las funciones más simples, las funciones lineales y las cuadráticas.<br />
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Funciones lineales o rectas:</h2>
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<span style="font-family: "verdana" , sans-serif;">Recordar que para representar rectas tenemos que hacer una tabla de valores con los valores de x que nosotros queramos, hallar las imágenes sustituyendo dicha x y después colocar los puntos en unos ejes de coordenadas y unirlos. El resultado no va a depender de los puntos que halláis elegido, será el mismo independientemente de ello. Es necesario utilizar como mínimo dos puntos aunque yo aconsejo que pongáis como mínimo tres para evitar errores de cálculo. Os dejo unos ejercicios con soluciones para que practiquéis:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgublB7x6p49Ph9YOdyQNQGab2eWuYQscVs6mw8ghQwpAlMKjP4ZcXyiE5KtsVmO6tni5UrKyDAtbN5NcdL8ATe0UVdvyVlmc_gY-GmfpCuCU4JTDblmT_olpGuJ4M1i-a3mJm8QDLBwa4/s1600/rectas+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="142" data-original-width="337" height="133" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgublB7x6p49Ph9YOdyQNQGab2eWuYQscVs6mw8ghQwpAlMKjP4ZcXyiE5KtsVmO6tni5UrKyDAtbN5NcdL8ATe0UVdvyVlmc_gY-GmfpCuCU4JTDblmT_olpGuJ4M1i-a3mJm8QDLBwa4/s320/rectas+1.png" width="320" /></a></div>
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<span style="font-family: "verdana" , sans-serif;"><b>SOLUCIONES: </b></span></div>
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<span style="font-family: "verdana" , sans-serif;">Las gráficas que os tienen que salir son estas:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-vRH2lv2uEFfbj4hW52mgvFA15a7SAfK6zBL8zTi-vLBKDEg1kPMa3WvKiKsFHyb1AltVyjNpu3Z1YaI_cT5XGT0po_Pl2OQ5IYWDq_7RJPUuI12dUxqbFe_pZW001G43UHmgJ-mzWkU/s1600/rectas+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="524" data-original-width="623" height="537" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-vRH2lv2uEFfbj4hW52mgvFA15a7SAfK6zBL8zTi-vLBKDEg1kPMa3WvKiKsFHyb1AltVyjNpu3Z1YaI_cT5XGT0po_Pl2OQ5IYWDq_7RJPUuI12dUxqbFe_pZW001G43UHmgJ-mzWkU/s640/rectas+2.png" width="640" /></a></div>
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<span style="font-family: "verdana" , sans-serif;">Funciones cuadráticas:</span></h2>
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<span style="font-family: "verdana" , sans-serif;">También las vimos el año pasado pero son un poco más largas por lo que os aconsejo que veáis el siguiente vídeo para recordarlo. Además para que quede claro coger lápiz y papel y en vuestro cuaderno hacéis el ejemplo que aparece en el vídeo. </span><br />
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Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-74694142642816356662020-05-29T03:21:00.002-07:002020-06-02T01:35:11.475-07:0029 MAYO 2020<span style="font-family: "verdana" , sans-serif;"><br /></span>
<span style="font-family: "verdana" , sans-serif;">Buenos días, adjunto ejercicios de dominios con solución. Solamente deberéis de hacer cinco apartados, uno de funciones polinómicas, otro de racionales, otro de raíz impar, otro de raíz par y otro de logaritmos. Aparecen muchos más, alguno de los cuales ya de nivel experto, si a alguien le apetece que lo intente y si tiene dudas yo se las resuelvo. Gracias y buen finde.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhy5ZzD6_unaTY6blPqnjafsSG9DllDjkv2cM3rjsJnP2pE_6CYCVBRcimGXg76wbzLVtcniYNNjJZVGfBgDhEuY-Vk1XGFWVuWtg4dE8QSOw0Khb9XEgSMXsaW3zdSc7tyRi_biO_0Krkr/s1600/dominios.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="505" data-original-width="925" height="349" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhy5ZzD6_unaTY6blPqnjafsSG9DllDjkv2cM3rjsJnP2pE_6CYCVBRcimGXg76wbzLVtcniYNNjJZVGfBgDhEuY-Vk1XGFWVuWtg4dE8QSOw0Khb9XEgSMXsaW3zdSc7tyRi_biO_0Krkr/s640/dominios.png" width="640" /></a></div>
<br />Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-60308447703952152242020-05-27T02:17:00.002-07:002020-05-27T03:07:07.136-07:0027 MAYO 2020<br />
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<span style="font-family: "verdana" , sans-serif;">Buenos días, hoy os propongo unos ejercicios de repaso de dominios, solamente tenéis que hacer un par de apartados de cada caso, el resto es por si no lo tenéis claro para que le echéis un vistazo:</span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: large;"><b>Calcula el dominio de las siguientes funciones racionales:</b></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"> </span><span style="font-family: "verdana" , sans-serif; font-size: small;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">1</span> <img alt="Función racional con denominador lineal " class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-11.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /> <span style="font-family: "verdana" , sans-serif; font-size: small;"> </span><span style="font-family: "verdana" , sans-serif; font-size: small;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">2</span> <img alt="Función racional con denominador de diferencia de cuadrados" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-12.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></span><br />
<span style="font-family: "verdana" , sans-serif; font-size: small;"><span style="font-family: "verdana" , sans-serif; font-size: small;"><span style="font-family: "verdana" , sans-serif; font-size: small;"> </span><span style="font-family: "verdana" , sans-serif; font-size: small;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">3</span> <img alt="Función racional con denominador cuadrático" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-13.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /> </span></span></span><span style="font-family: "verdana" , sans-serif; font-size: small;"> </span><span style="font-family: "verdana" , sans-serif; font-size: small;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">4</span> <img alt="Función racional con trinomio como denominador" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-14.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span><br />
<span style="font-family: "verdana" , sans-serif; font-size: small;"><span style="font-family: "verdana" , sans-serif; font-size: small;"> </span><span style="font-family: "verdana" , sans-serif; font-size: small;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">5</span> <img alt="Función racional con denominador de trinomio cuadrado perfecto " class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-15.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /> </span></span><span style="font-family: "verdana" , sans-serif; font-size: small;"> </span><span style="font-family: "verdana" , sans-serif; font-size: small;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">6</span> <img alt="Función racional con polinomio como denominador" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-16.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">7</span> <img alt="Función racional con polinomio grado 4 como denominador " class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-17.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"> </span><span style="background-color: #fff4f6; color: #fa6484; font-family: "verdana" , sans-serif; font-size: small; font-style: inherit; font-weight: 600;">Solución</span><br />
<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif; font-size: small;"> </span><span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "verdana" , sans-serif; font-size: small; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">1</span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif; font-size: small;"> </span><img alt="Función racional con denominador lineal " class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; font-size: medium; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /><br />
<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif; font-size: small;"> </span><i style="background-color: #fff4f6;"><span style="font-family: "verdana" , sans-serif; font-size: small;">El dominio de una función racional es</span><span style="font-family: "verdana" , sans-serif; font-size: small;"> </span><span style="background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; font-size: small; margin: 0px; padding: 0px;">ℛ </span><span style="font-family: "verdana" , sans-serif; font-size: small;">menos los valores que anulan al denominador.</span><span style="font-family: "verdana" , sans-serif; font-size: small;"> </span></i><br />
<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif; font-size: small;">Tenemos que igualar el denominador a cero y resolver la ecuación.</span><br />
<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif; font-size: small;">Las soluciones a la ecuación son los puntos que no pertenecen al Dominio de la función.</span><br />
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<img alt="El dominio es el conjunto de los reales a excepción del -2" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-2.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; font-size: medium; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /><br />
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<span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: verdana, sans-serif; font-size: small; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; width: 30px;">2</span><span style="background-color: #fff4f6; font-family: verdana, sans-serif; font-size: small; text-align: justify;"> </span><img alt="Función racional con denominador de diferencia de cuadrados" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-3.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; font-size: medium; height: auto; margin: 0px; max-width: 100%; padding: 0px; text-align: justify;" /></div>
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<img alt="El dominio es el conjunto de los reales a excepción de -1 y 1" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-4.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; font-size: medium; height: auto; margin: 0px; max-width: 100%; padding: 0px; text-align: center;" /></div>
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<span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: verdana, sans-serif; font-size: small; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">3</span><span style="background-color: #fff4f6; font-family: verdana, sans-serif; font-size: small;"> </span><img alt="Función racional con denominador cuadrático" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-5.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; font-size: medium; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><img alt="El dominio es el conjunto de los reales" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-6.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;">Como esta ecuación no tiene raíces reales el dominio es </span><span style="background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; font-size: small; margin: 0px; padding: 0px;">ℛ</span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">4</span> <img alt="Función racional con trinomio como denominador" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-7.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><img alt="El dominio es el conjunto de los reales a excepción de -1" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-8.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<div style="background-repeat: no-repeat; box-sizing: inherit; font-weight: 400; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px; text-align: justify;">
<span style="font-family: "verdana" , sans-serif; font-size: small;">Como está ecuación tiene una raíz doble, el único elemento que anula el denominador es el -1.</span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">5</span> <img alt="Función racional con denominador de trinomio cuadrado perfecto " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-9.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;">Igualamos a cero el denominador y resolvemos la ecuación</span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><img alt="Trinomio cuadrado perfecto " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-10.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><img alt="Formula general para resolver ecuaciones de segundo grado " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-11.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><img alt="El dominio es el conjunto de los reales a excepción de 2 y 3" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-12.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">6</span> <img alt="Función racional con polinomio como denominador" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-13.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
<div style="background-repeat: no-repeat; box-sizing: inherit; font-weight: 400; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px; text-align: justify;">
<span style="font-family: "verdana" , sans-serif; font-size: small;">Si factorizamos mediante Ruffini la única solución es el -1.</span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><img alt="El dominio es el conjunto de los reales a excepción de -1" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-14.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<div style="background-repeat: no-repeat; box-sizing: inherit; font-weight: 400; hyphens: none; line-height: 3rem; margin-bottom: 1rem; padding: 0px; text-align: justify;">
<span style="font-family: "verdana" , sans-serif; font-size: small;">Como está ecuación tiene una raíz triple, el único elemento que no pertenece al dominio es –1</span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">7</span> <img alt="Función racional con polinomio grado 4 como denominador " class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-15.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><img alt="Denominador de la función " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-16.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><img alt="Factorizacion del denominador " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-17.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;"><img alt="El dominio es el conjunto de los reales a excepción de -3, -3 ,2,3" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-2-18.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: large;"><b>Calcular el dominio de las funciones radicales :</b></span></span></div>
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<span style="font-family: "verdana" , sans-serif; font-size: small;">a) Índice impar:</span><br />
<span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "verdana" , sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">1</span><span style="font-family: "verdana" , sans-serif;"> </span><img alt="Función con radical cubico " class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-18.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /> <span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "verdana" , sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">2</span><span style="font-family: "verdana" , sans-serif;"> </span><img alt="Función racional con radical cubico" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-19.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /><br />
<span style="font-family: "verdana" , sans-serif; font-size: small;"> </span><span style="background-color: #fff4f6; color: #fa6484; font-family: "verdana" , sans-serif; font-size: small; font-style: inherit; font-weight: 600;">Solución</span><br />
<span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "verdana" , sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">1</span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><img alt="Función con radical cubico " class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-3.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /><br />
<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif; font-size: small;">Las raíces de índice impar no ofrecen problemas, nos tenemos que fijar en lo que hay dentro. Como dentro tenemos un polinimio entonces el dominio es </span><span style="background-color: #fff4f6; background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; font-size: small; margin: 0px; padding: 0px;">ℛ</span><br />
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<img alt="El dominio es el conjunto de los reales" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-3-2.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "verdana" , sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; width: 30px;">2</span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><img alt="Función racional con radical cubico" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-3-3.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;">La raíz cúbica no ofrece problemas pero el denominador sí por lo que hallamos los valores que anulan el denominador.</span></div>
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<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;">x + 1 = 0 </span><span style="background-color: #fff4f6; background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; margin: 0px 0px 0px 3%; padding: 0px;">x = –1</span></div>
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<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif; font-size: small; text-align: justify;"> </span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif; font-size: small;"><img alt="El dominio es el conjunto de los reales a excepción de -1" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-3-4.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif;">b) Funciones radicales de índice par:</span></div>
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<span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "poppins" , "helvetica neue" , "helvetica" , "arial" , sans-serif; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">1</span><span style="background-color: #f7f7f7; font-family: "verdana" , sans-serif;"><b>2</b></span><span style="font-family: "verdana" , sans-serif;"> </span><span style="background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; height: auto;"><img alt="Función radical de un trinomio de grado 2" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-23.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /> 2</span><span style="font-family: "verdana" , sans-serif; font-weight: 600;"><span style="font-weight: 400;"> </span><img alt="Función radical simple" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-21.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-weight: 400; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="background-color: #f7f7f7;"><b>3</b></span><span style="background-color: white; font-weight: 400;"> </span></span><img alt="Función racional con denominador radical " class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-30.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: Verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /><span style="font-family: "verdana" , sans-serif;"><span style="background-color: white;"> </span></span><span style="background-color: #f7f7f7; font-family: "verdana" , sans-serif;"><b>4</b></span><span style="background-color: white; font-family: "verdana" , sans-serif;"> </span><span style="font-family: "verdana" , sans-serif;"><span style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; height: auto;"><img alt="Función radical de un trinomio de grado 3" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-29.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="background-color: #f7f7f7;"><b>5</b></span><span style="background-color: white; font-weight: 400;"> </span><span style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; height: auto;"><img alt="Función radical y racional por el numerador" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-32.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-weight: 400; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /> </span></span><span style="background-color: #f7f7f7; font-family: "verdana" , sans-serif;"><b>6</b></span><span style="background-color: white; font-family: "verdana" , sans-serif;"> </span><span style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; height: auto;"><img alt="Función radical y racional " class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-34.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; height: auto;"><span style="background-color: #fff4f6; color: #fa6484; font-style: inherit; font-weight: 600;">Solución</span><span style="background-color: #fff4f6;"> </span></span></div>
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<span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "verdana" , sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">1</span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><img alt="Función radical simple" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: Verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /><br />
<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;">El dominio de una función irracional de índice par está formado por todos los valores que hacen que el radicando sea positivo o cero.</span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><br />
<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;">Por tanto hacemos el radicando mayor o igual a cero y </span><a href="https://www.superprof.es/apuntes/escolar/matematicas/algebra/inecuaciones/inecuaciones-de-segundo-grado-y-racionales.html" style="background-repeat: no-repeat; box-sizing: inherit; color: #444444; font-family: verdana, sans-serif; margin: 0px; padding: 0px; transition: all 0.2s ease 0s;">resolvemos la inecuación</a><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span></div>
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<img alt=" El dominio va de 2 hasta infinito " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-2.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: Verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="background-color: #f7f7f7; font-family: "verdana" , sans-serif;">2</span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><span style="background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; height: auto;"><img alt="Función radical de un trinomio de grado 2" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-5.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span><br />
<span style="background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; height: auto;"><span style="background-color: #fff4f6; text-align: center;"> x² – 6x + 8 ≥ 0</span></span></div>
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<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;">Igualamos a cero para encontrar las raíces de la ecuación</span></div>
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<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;">x² – 6x + 8 = 0 </span></div>
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<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;">Resolvemos la ecuación y las raíces son 2 y 4</span></div>
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<img alt="Representación gráfica de valores que no son parte del dominio " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-6.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;">Tiene que ser mayor (tomamos los intervalos con el signo +) o igual a cero</span></div>
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<img alt="El dominio es una unión de conjuntos" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-7.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><span style="background-color: #f7f7f7; font-family: "verdana" , sans-serif;">3</span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><span style="background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; height: auto;"><img alt="Función radical de un trinomio de grado 3" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-19.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; height: auto;"><span style="background-color: #fff4f6;"> </span><img src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-20.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; height: auto;"><span style="background-color: #fff4f6;"> </span><img alt="Representación gráfica de valores que no son parte del dominio " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-21.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; height: auto;"><span style="background-color: #fff4f6;"> </span><img alt="El dominio es una unión de conjuntos " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-22.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; height: auto;"><span style="background-color: #fff4f6;"> </span><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">4</span><span style="background-color: #fff4f6;"> </span><img alt="Función racional con denominador radical " class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-23.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="background-repeat: no-repeat; box-sizing: inherit; font-family: "verdana" , sans-serif; height: auto;"><span style="background-color: #fff4f6;"> </span><span style="background-color: #fff4f6;">Por estar la raíz en el denominador, el radicando tiene que ser mayor que 0</span></span></div>
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<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><img alt="El dominio va de 2 hasta infinito" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-24.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: Verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "verdana" , sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">5</span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><img alt="Función radical y racional por el numerador" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-27.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: Verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /><br />
<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif; text-align: center;"> </span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif; text-align: center;">El numerador tiene que se mayor o igual que cero y el denominador no puede ser 0.</span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif; text-align: center;"> </span><br />
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<img alt="Sistema de ecuaciones para encontrar el dominio de la función " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-28.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px; text-align: center;" /><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif; text-align: center;"></span><br />
<img alt="Representación gráfica de valores que no son parte del dominio " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-29.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px; text-align: center;" /></div>
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<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><span style="background-color: #fff4f6; color: #fa6484; font-family: "verdana" , sans-serif; font-weight: 600;">D = (–∞, 4) ∪ (–4, 2] ∪[3, ∞)</span></div>
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<span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "verdana" , sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">6</span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><img alt="Función radical y racional por el denominador" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-34.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: Verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> </span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;">El radicando tiene que ser mayor que cero y el denominador distinto</span><span style="background-color: #fff4f6; font-family: "verdana" , sans-serif;"> de cero</span><img alt="Trabajo algebraico en la función " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-35.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<img alt="Representación gráfica de valores que no son parte del dominio " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-36.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; color: #fa6484; font-family: verdana, sans-serif; font-weight: 600; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<img alt="El dominio es una unión de conjuntos " class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-4-37.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="background-color: white; font-family: "open sans" , "helvetica neue" , "helvetica" , "arial" , sans-serif;"><span style="font-size: large;"><b>Calcular el dominio de las funciones logarítmicas:</b></span></span><br />
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<span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "poppins" , "helvetica neue" , "helvetica" , "arial" , sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">1</span> <img alt="Función logarítmica" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-37.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "poppins" , "helvetica neue" , "helvetica" , "arial" , sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">2</span> <img alt="Función logarítmica racional " class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-38.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="background-color: #fff4f6; color: #fa6484; font-family: inherit; font-style: inherit; font-weight: 600;">Solución</span></div>
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<span style="background-color: #fff4f6;">Calcular el dominio de las funciones logarítmicas:</span></div>
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<span style="background-color: #fff4f6;"> </span><span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "poppins" , "helvetica neue" , "helvetica" , "arial" , sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">1</span><span style="background-color: #fff4f6;"> </span><img alt="Función logarítmica" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-6.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /><span style="background-color: #fff4f6;"> </span></div>
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<span style="background-color: #fff4f6;">Para que exista el logaritmo la función tiene que ser mayor que cero </span></div>
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<img alt="El dominio va de 2 hasta infinito" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-6-2.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "poppins" , "helvetica neue" , "helvetica" , "arial" , sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; width: 30px;"><br /></span></div>
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<span class="sb" style="background: rgb(247 , 247 , 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: "poppins" , "helvetica neue" , "helvetica" , "arial" , sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; width: 30px;">2</span><span style="background-color: #fff4f6; text-align: left;"> </span><img alt="Función logarítmica racional " class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-6-3.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px; text-align: left;" /><span style="background-color: #fff4f6; text-align: left;"> </span></div>
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<span style="background-color: #fff4f6; text-align: center;">Como el denominador es siempre positivo, tan solo estudiamos el numerador</span></div>
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<img alt="El dominio va de 0 hasta infinito" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-6-4.gif" style="background-color: #fff4f6; background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px; text-align: center;" /></div>
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Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-61364614757025775492020-05-25T16:15:00.001-07:002020-05-25T16:16:08.308-07:0025 MAYO 2020<div style="text-align: justify;">
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<span style="font-family: "verdana" , sans-serif;">Buenos días chic@s, hoy vamos a ver el domino de las funciones LOGARÍTMICAS. Recordamos que solamente se pueden hallar logaritmos de números positivos, no se puede hallar logaritmos de números negativos ni de 0. Aquí igual que en la funciones racionales de radicando par también tenemos que utilizar las inecuaciones.</span></div>
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<span style="font-family: "verdana" , sans-serif;">Los ejercicios que os propongo son los que aparecen en el vídeo así que lo que tenéis que hacer es ver el vídeo y hacerlos en vuestro cuaderno.</span><br />
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</span>Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-78804859336545591262020-05-21T15:52:00.001-07:002020-05-21T15:52:58.546-07:0022 MAYO 2020<span style="font-family: Verdana, sans-serif;"><br /></span>
<span style="font-family: Verdana, sans-serif;">Buenos días chic@s, hoy vamos a ver el domino de las funciones racionales. Si recordáis la parte de inecuaciones aquí las tendremos que usar. Recordad que lo más importante es entender los conceptos para poder hacer los ejercicios y que ante cualquier duda solo tenéis que planteármela en el mail. </span><br />
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<span style="font-family: Verdana, sans-serif;">Los ejercicios que os propongo son los que aparecen en el vídeo así que lo que tenéis que hacer es ver el vídeo y hacerlos en vuestro cuaderno</span><br />
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<span style="font-family: Verdana, sans-serif;">Buen finde!</span></div>
<span style="font-family: Verdana, sans-serif;"><br /></span>Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-17049024979712938692020-05-19T14:55:00.003-07:002020-05-19T14:55:31.510-07:0020 MAYO 2020<br />
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<span style="font-family: Verdana, sans-serif;">Buenos días chic@s, hoy vamos a hacer algunos ejercicios de cálculo de dominios. Para ello tenemos que tener muy claro el concepto de dominio de una función. Recordemos que el dominio de una función es el conjunto de valores de la variable independiente x que tienen imagen. Cuando la función viene dada por una expresión analítica o fórmula la imagen de un punto x se obtiene sustituyendo el valor de la x en la expresión pero tenemos que tener en cuenta que hay ciertas operaciones en matemáticas que <b>no</b> se pueden realizar como:</span></div>
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<li><span style="font-family: Verdana, sans-serif;"> dividir por cero</span></li>
<li><span style="font-family: Verdana, sans-serif;"> hacer raíces pares de números negativos </span></li>
<li><span style="font-family: Verdana, sans-serif;"> o logaritmos de números negativos o cero </span></li>
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<span style="font-family: Verdana, sans-serif;">Esto es lo que determina la manera de hallar el dominio según el tipo de expresión que es lo que clasificamos en la entrada del día anterior en casos. Os recomiendo que los volváis a ver para hacer los ejercicios y entenderlos. </span><br />
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<h3 style="background-repeat: no-repeat; box-sizing: inherit; color: #222222; font-family: Poppins, "Helvetica Neue", Helvetica, Arial, sans-serif; margin: 0px; padding: 0px;">
<span style="font-size: large;">Dominio en funciones polinómicas</span></h3>
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<span style="font-family: Verdana, sans-serif;"> Recordamos que las funciones polinómicas no tienen operaciones que presenten problemas (son sumas, restas, productos y potencias) por lo que su dominio serían todos los números reales. Por lo tanto hallar el dominio en una función polinómica es un trivialidad, veamos:</span></div>
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<h2 id="tema_dominio-en-funciones-polinomicas" style="background-repeat: no-repeat; box-sizing: inherit; font-family: Poppins, "Helvetica Neue", Helvetica, Arial, sans-serif; margin: 0px; padding: 0px;">
<span style="font-size: small;"><span style="font-family: Verdana, sans-serif;"> </span><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: Verdana, sans-serif; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">1</span><span style="font-family: Verdana, sans-serif;"> </span><span style="font-family: Verdana, sans-serif;"><b>f(x)= x² – 5x + 6</b></span></span></h2>
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<span style="font-family: Verdana, sans-serif;"> <span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">2</span> <img alt="Función polinómica de grado 5" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: Verdana, sans-serif;"> <span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">3</span> <img alt="Función polinómica de grado 2" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-10.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="background-color: #fff4f6; color: #fa6484; font-family: inherit; font-size: inherit; font-style: inherit; font-variant-caps: inherit; font-variant-ligatures: inherit; font-weight: 600;">Solución</span></div>
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<span style="font-family: Verdana, sans-serif;">Calcular el dominio de las funciones polinómicas:</span></div>
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<span style="font-family: Verdana, sans-serif;"> </span><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: Verdana, sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">1</span><span style="font-family: Verdana, sans-serif;"> </span><span style="font-family: Verdana, sans-serif;">f(x)= x² – 5x + 6</span></div>
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<span style="font-family: Verdana, sans-serif;"> </span><span style="font-family: Verdana, sans-serif;">El dominio de una función polinómica entera es</span><span style="font-family: Verdana, sans-serif;"> </span><span style="background-repeat: no-repeat; box-sizing: inherit; font-family: Verdana, sans-serif; margin: 0px; padding: 0px;">ℛ</span></div>
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<span style="font-family: Verdana, sans-serif;"> </span><img alt="El dominio es el conjunto de los reales." class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-1.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: Verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="font-family: Verdana, sans-serif;"> </span><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: Verdana, sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">2</span><span style="font-family: Verdana, sans-serif;"> </span><img alt="Función polinómica de grado 5" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-1-2.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: Verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="font-family: Verdana, sans-serif;"> </span><img alt="El dominio es el conjunto de los reales." class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-1-3.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: Verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="font-family: Verdana, sans-serif;"> </span><span class="sb" style="background: rgb(247, 247, 247); border-radius: 50%; box-sizing: inherit; display: inline-block; font-family: Verdana, sans-serif; font-weight: 700; height: 30px; line-height: 30px; margin: 0px 1rem 0px 0px; padding: 0px; text-align: center; width: 30px;">3</span><span style="font-family: Verdana, sans-serif;"> </span><img alt="Función polinómica de grado 2" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-1-4.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: Verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="font-family: Verdana, sans-serif;"> </span><span style="font-family: Verdana, sans-serif;">Esta función también es polinómica entera porque no tiene</span><span style="font-family: Verdana, sans-serif;"> </span><em style="background-repeat: no-repeat; box-sizing: inherit; font-family: Verdana, sans-serif; margin: 0px; padding: 0px;">x</em><span style="font-family: Verdana, sans-serif;"> </span><span style="font-family: Verdana, sans-serif;">en </span><span style="font-family: Verdana, sans-serif;">el denominador, se puede escribir como:</span></div>
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<span style="font-family: Verdana, sans-serif;"><img alt="Función polinómica de grado 2" class="i alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-1-5.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></span></div>
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<span style="font-family: Verdana, sans-serif;"> Por lo tanto: </span><img alt="El dominio es el conjunto de los reales." class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-del-dominio-de-una-funcion-1-6.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: Verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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<span style="font-family: Verdana, sans-serif;"> Ya véis, el dominio de una función polinómica son todos los números reales.</span></div>
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<span style="font-family: Poppins, "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: large;"><b>Dominio en funciones racionales:</b></span></div>
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<span style="font-family: Verdana, sans-serif;">Las funciones racionales son las que tienen x en el denominador, recordad que en matemáticas no se puede dividir por cero.</span></div>
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Tenéis que hacer en vuestro cuaderno los ejercicios que aparecen el el siguiente vídeo</div>
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Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-72460290401075510332020-05-17T15:21:00.002-07:002020-05-18T02:47:26.025-07:0018 MAYO 2020<br />
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<span style="font-family: "verdana" , sans-serif;">Buenos días chic@s, vamos a ver un poco de funciones, recordad que el curso pasado ya vimos el concepto de función, interpretamos gráficas y aprendimos a representar las funciones lineales y la funciones cuadráticas. El estudio de las funciones es algo básico y fundamental en las matemáticas con infinidad de aplicaciones en diferentes campos desde la economía, física, ingeniería, biología, sociología etc (<b><span style="color: blue;"><i><a href="https://prezi.com/tbqkv_yg3ara/aplicaciones-de-las-funciones-en-la-vida-cotidiana/">aqui</a></i> </span></b>os dejo unos ejemplos). Vamos a recordarlo y a avanzar un poco:</span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><b>Concepto de función:</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><span style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; font-size: 16px; margin: 0px; padding: 0px;">Una <b><u>función</u></b> es una relación entre dos magnitudes, de tal manera que a cada valor de la primera le corresponde un único valor de la segunda, llamada imagen. A la primera magnitud se le representa por la variable <b>x</b>, llamada variable independiente y a la segunda por la variable<b> y</b> o <b>f(x)</b> denominada variable dependiente puesto que su valor depende de x.</span></span></div>
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<span style="color: #222222; font-family: "verdana" , sans-serif;"><span style="background-color: white;">Veamos un ejercicio:</span></span></div>
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<span style="color: #0b5394; font-family: "verdana" , sans-serif;"><i>Razonar si las siguientes relaciones son funciones.</i></span></div>
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<span style="color: #0b5394; font-family: "verdana" , sans-serif;"><i> a)<span class="Gris_NumApartados" style="box-sizing: border-box;"> </span>Cada número real y su doble.<br style="box-sizing: border-box;" /> b)<span class="Gris_NumApartados" style="box-sizing: border-box;"> </span>El tiempo que está un grifo abierto y la cantidad de agua que sale.<br style="box-sizing: border-box;" /> c)<span class="Gris_NumApartados" style="box-sizing: border-box;"> </span>El peso de cada persona según su altura.</i></span></div>
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<span style="box-sizing: border-box; font-weight: 700;"><span style="color: #0b5394; font-family: "verdana" , sans-serif;"><i>Solución</i></span></span></div>
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<span style="color: #0b5394; font-family: "verdana" , sans-serif; font-size: x-small;"><i><span class="Gris_NumApartados" style="box-sizing: border-box;"> a) </span>Es una función porque para cada valor de <span style="box-sizing: border-box;">x,</span> su doble es un único número.<br style="box-sizing: border-box;" /><span class="Gris_NumApartados" style="box-sizing: border-box;"> b) </span>Es una función porque según los minutos que está el grifo abierto obtenemos un número único de litros de agua recogida.<br style="box-sizing: border-box;" /><span class="Gris_NumApartados" style="box-sizing: border-box;"> c) </span>No es una función, porque para personas con la misma altura, podemos obtener varios </i></span><br />
<i style="color: #0b5394; font-family: verdana, sans-serif; font-size: small;"> valores distintos de peso.</i><br />
<i style="color: #0b5394; font-family: verdana, sans-serif; font-size: small;"><br /></i><span style="color: #274e13; font-family: "verdana" , sans-serif;">Os dejo un vídeo para aclarar más el concepto de función:</span><br />
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<span style="font-family: "verdana" , "arial" , "helvetica" , sans-serif; font-size: small;">A la función se le suele designar por <span style="color: #993366;"><b>f</b></span> y a la imagen por <span style="color: #993366;"><b>f(x)</b></span>, siendo x la variable independiente.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; font-family: "open sans" , "helvetica neue" , "helvetica" , "arial" , sans-serif; font-size: 16px; font-weight: bolder; margin: 0px; padding: 0px;"></span></span><br /></div>
<ul style="text-align: justify;"><span style="font-family: "verdana" , "arial" , "helvetica" , sans-serif; font-size: small;">
<li><span style="color: #993366; font-weight: bold;">Variable independiente:</span> la que se fija previamente</li>
<li><span style="color: #993366; font-weight: bold;">Variable dependiente:</span> La que se deduce de la variable independiente.</li>
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<span style="font-family: "verdana" , sans-serif;"><span style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; font-size: 16px; margin: 0px; padding: 0px;">Por tanto una función lo que hace es asignarle a cada valor de la variable independiente x un único valor de la variable dependiente y que llamamos imagen y representamos por f(x). Entonces genera pares de valores asociados, cada x</span><span style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; font-size: x-small; margin: 0px; padding: 0px;">o</span><span style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; font-size: 16px; margin: 0px; padding: 0px;"> con su imagen f(x</span><span style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; font-size: x-small; margin: 0px; padding: 0px;">o</span><span style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; font-size: 16px; margin: 0px; padding: 0px;">) y dichos valores puestos en unos ejes cartesianos generarán la gráfica de la función.</span></span><br />
<span style="font-family: "verdana" , sans-serif;"><span style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; font-size: 16px; margin: 0px; padding: 0px;"><br /></span></span>
<span style="font-family: "verdana" , sans-serif;"><span style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; font-family: "verdana" , sans-serif; margin: 0px; padding: 0px;"><b style="text-align: left;">Expresión analítica</b><span style="text-align: left;">. La </span><b style="text-align: left;">expresión analítica</b><span style="text-align: left;"> de una </span><b style="text-align: left;">función</b><span style="text-align: left;"> es una ecuación que relaciona la variable dependiente con la variable independiente, es decir, una expresión que me permite hallar la imagen de cada valor de la variable independiente x sin más que sustituir la x por su valor.</span></span></span><br />
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<span style="color: #222222; font-family: "verdana" , sans-serif;"><span style="background-color: white;">Por ejemplo:</span></span></div>
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<span style="color: #222222; font-family: "verdana" , sans-serif;"><span style="background-color: white;">a) f(x)=2x-1, la función viene expresada por la expresión analítica 2x-1 </span></span></div>
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<span style="color: #222222; font-family: "verdana" , sans-serif;"><span style="background-color: white;">¿Cual sería la imagen de x=1?</span></span></div>
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<span style="color: #222222; font-family: "verdana" , sans-serif;"><span style="background-color: white;"><br /></span></span></div>
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<span style="color: #222222; font-family: "verdana" , sans-serif;"><span style="background-color: white;">Pues la obtendría sustituyendo x por 1, es decir, f(1)=2·1-1=1</span></span></div>
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<span style="color: #222222; font-family: "verdana" , sans-serif;"><span style="background-color: white;"><br /></span></span></div>
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<span style="color: #222222; font-family: "verdana" , sans-serif;"><span style="background-color: white;">¿Y la imagen del 3?</span></span></div>
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<span style="color: #222222; font-family: "verdana" , sans-serif;"><span style="background-color: white;"> f(3)=2·3-1=5</span></span><br />
<span style="color: #222222; font-family: "verdana" , sans-serif;"><span style="background-color: white;"><br /></span></span>
<span style="color: #222222; font-family: "verdana" , sans-serif;"><span style="background-color: white;">b)</span></span><img alt="imagen de una funcion ejemplos" src="https://ekuatio.com/wp-content/uploads/imagen-de-una-funci%C3%B3n-9.png" /><br />
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<span style="font-family: "verdana" , sans-serif;">¿Cuál sería la imagen de x=7?</span></div>
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<span style="color: #222222; font-family: "verdana" , sans-serif;"><span style="background-color: white;"><br /></span></span>
<span style="color: #222222; font-family: "verdana" , sans-serif;"><span style="background-color: white;">Pues tenemos que cambiar la x por 7 y obtenemos f(7)=</span></span><span style="text-align: justify;">3</span><br />
<span style="text-align: justify;"><br /></span>
<span style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">¿Y la imagen de -6?</span></span><br />
<span style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;"><br /></span></span>
<span style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">Sustituyendo la x por -6 obtenemos la raíz de - 4, que no tiene solución!!</span></span><br />
<span style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;"><br /></span></span>
<span style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;">Esto nos lleva a pensar que en algunos casos no siempre todos los puntos tienen imagen y por eso vamos a tener que introducir un concepto nuevo que es el de <b><i>dominio de definición de una función</i></b></span></span><br />
<span style="text-align: justify;"><span style="font-family: "verdana" , sans-serif;"><b><i><br /></i></b></span></span>
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<span style="font-family: "verdana" , sans-serif;"><i>El dominio de una función está formado por todos los valores de x que tienen imagen.</i></span></div>
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<span style="font-family: "verdana" , sans-serif;">Es decir, son los valores de x que podemos sustituir en la expresión analítica de la función para obtener el valor correspondiente de f(x).</span><br />
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<span style="font-family: "verdana" , sans-serif;">Veamos una breve explicación para después definir unas reglas para poder hallar dominios de funciones:</span></div>
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<span style="color: #274e13;"><iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/lmfDEGDpgV8/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/lmfDEGDpgV8?feature=player_embedded" width="320"></iframe></span></div>
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<div style="background: rgb(255, 255, 255); border: 0px; line-height: 1.5em; margin: 0px 0px 25px; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
<span style="background: transparent; border: 0px; font-weight: normal; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13; font-family: Verdana, sans-serif; font-size: small;">Entonces el dominio tiene que ver con la forma que tenga la expresión analítica, con que hay ciertas operaciones que en matemáticas no se pueden hacer. Esas operaciones son las que nos van a determinar como podemos hallar el dominio de una función</span></span></div>
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<span style="background-color: transparent; font-size: 22.652px;">Cuándo una función no existe</span></h2>
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Una función no existirá cuando para los valores de x que provoquen los siguientes casos:</div>
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<span id="1-_Cuando_un_numeroquede_dividido_entre_0" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">1- Cuando un número quede dividido entre 0:</span></h3>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="como calcular el dominio de una función" class="aligncenter wp-image-5900 size-full lazyloaded" data-lazy-sizes="(max-width: 305px) 100vw, 305px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-1.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-1.png 305w, https://ekuatio.com/wp-content/uploads/dominio-1-300x237.png 300w, https://ekuatio.com/wp-content/uploads/dominio-1-100x79.png 100w" data-was-processed="true" height="241" loading="lazy" sizes="(max-width: 305px) 100vw, 305px" src="https://ekuatio.com/wp-content/uploads/dominio-1.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-1.png 305w, https://ekuatio.com/wp-content/uploads/dominio-1-300x237.png 300w, https://ekuatio.com/wp-content/uploads/dominio-1-100x79.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="305" /></div>
<h3 style="background: rgb(255, 255, 255); border: 0px; color: #333333; font-family: Raleway, sans-serif; font-size: 1.387em; line-height: 1.5em; margin: 0px 0px 0.5em; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
<span id="2-_Cuando_el_contenido_de_una_raiz_de_indice_par_es_un_numero_negativo" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">2- Cuando el contenido de una raíz de índice par es un número negativo</span></h3>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="dominio de una función" class="aligncenter wp-image-5899 size-full lazyloaded" data-lazy-sizes="(max-width: 178px) 100vw, 178px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-2.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-2.png 178w, https://ekuatio.com/wp-content/uploads/dominio-2-100x52.png 100w" data-was-processed="true" height="93" loading="lazy" sizes="(max-width: 178px) 100vw, 178px" src="https://ekuatio.com/wp-content/uploads/dominio-2.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-2.png 178w, https://ekuatio.com/wp-content/uploads/dominio-2-100x52.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="178" /></div>
<h3 style="background: rgb(255, 255, 255); border: 0px; color: #333333; font-family: Raleway, sans-serif; font-size: 1.387em; line-height: 1.5em; margin: 0px 0px 0.5em; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
<span id="3-_Cuando_el_contenido_de_un_logaritmo_es_0_o_un_numero_negativo" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">3- Cuando el contenido de un logaritmo es 0 o un número negativo</span></h3>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="dominio de una función" class="aligncenter wp-image-5898 size-full lazyloaded" data-lazy-sizes="(max-width: 192px) 100vw, 192px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-3.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-3.png 192w, https://ekuatio.com/wp-content/uploads/dominio-3-100x45.png 100w" data-was-processed="true" height="86" loading="lazy" sizes="(max-width: 192px) 100vw, 192px" src="https://ekuatio.com/wp-content/uploads/dominio-3.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-3.png 192w, https://ekuatio.com/wp-content/uploads/dominio-3-100x45.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="192" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Ahora que ya sabes que una función puede tener un valor para unos valores de x o puede no existir para otros valores de x, voy a pasar a explicarte qué es el dominio de una función.</div>
<h2 style="background: rgb(255, 255, 255); border: 0px; color: rgb(37, 187, 142) !important; font-family: Raleway, sans-serif; font-size: 1.618em; line-height: 1.5em; margin: 0px 0px 25px; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
<span id="Que_es_el_dominio_de_una_funcion" style="background: transparent; border: 0px; font-size: 22.652px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Volvemos a repetir: ¿Qué es el dominio de una función?</span></h2>
<div class="woo-sc-box normal " style="background: none rgba(24, 200, 147, 0.17); border-radius: 0.327em; border: 2px solid rgb(24, 200, 147); color: #555555; font-family: Raleway, sans-serif; font-size: 14px; margin: 1em 0px 1.5em; outline: 0px; padding: 9px 15px; text-shadow: none; vertical-align: baseline;">
El <strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">dominio de una función</strong> <strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">es el rango de valores de x para los que existe f(x), es decir, los valores de x, para los que f(x) tiene un resultado.</strong></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
</div>
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Se designa como Dom f.</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
Visto así asusta un poco, pero conforme vayamos resolviendo ejemplos te va a ir quedando mucho más claro.</div>
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Para calcular el dominio de una función, debemos obtener los valores de x, para los que exista esa función. O dicho de otra forma, debemos encontrar para qué valores de x, la función no existe y quedarnos con los valores de x donde la función sí existe.</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
El dominio de una función entonces depende mucho del tipo de función.</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Vamos a verlo:</div>
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<span id="Como_calcular_el_dominio_de_una_funcion" style="background: transparent; border: 0px; font-size: 22.652px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Cómo calcular el dominio de una función</span></h2>
<h3 style="background: rgb(255, 255, 255); border: 0px; color: #333333; font-family: Raleway, sans-serif; font-size: 1.387em; line-height: 1.5em; margin: 0px 0px 0.5em; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
<span id="Dominio_de_una_funcion_polinomica" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Dominio de una función polinómica</span></h3>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Las funciones polinómicas son en las que no aparecen ni denominadores ni raíces.</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
La x puede aparecer sumando, restando, multiplicando o elevada a algún exponente, como por ejemplo:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="dominio de una función ejercicios resueltos" class="aligncenter wp-image-5901 size-full lazyloaded" data-lazy-sizes="(max-width: 149px) 100vw, 149px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-4.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-4.png 149w, https://ekuatio.com/wp-content/uploads/dominio-4-100x59.png 100w" data-was-processed="true" height="88" loading="lazy" sizes="(max-width: 149px) 100vw, 149px" src="https://ekuatio.com/wp-content/uploads/dominio-4.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-4.png 149w, https://ekuatio.com/wp-content/uploads/dominio-4-100x59.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="149" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
En este tipo de funciones no existe ningún valor de x que haga que f(x) no exista. Por tanto, f(x) existe siempre.</div>
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Cuando una función existe siempre, su dominio es todo el conjunto de los números reales:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="dominio de una función ejercicios" class="aligncenter wp-image-5906 size-full lazyloaded" data-lazy-sizes="(max-width: 107px) 100vw, 107px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-5.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-5.png 107w, https://ekuatio.com/wp-content/uploads/dominio-5-100x26.png 100w" data-was-processed="true" height="28" loading="lazy" sizes="(max-width: 107px) 100vw, 107px" src="https://ekuatio.com/wp-content/uploads/dominio-5.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-5.png 107w, https://ekuatio.com/wp-content/uploads/dominio-5-100x26.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="107" /></div>
<h3 style="background: rgb(255, 255, 255); border: 0px; color: #333333; font-family: Raleway, sans-serif; font-size: 1.387em; line-height: 1.5em; margin: 0px 0px 0.5em; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
<span id="Como_se_calcula_el_dominio_de_una_funcion_racional" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Cómo se calcula el dominio de una función racional</span></h3>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Las funciones racionales existen para todo R, menos para los valores que hacen 0 el denominador.</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Por tanto, para calcular el dominio de una función racional, debemos encontrar los valores que hacen 0 el denominador y quitárselo a R.</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Por ejemplo:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="como se calcula el dominio de una función" class="aligncenter wp-image-5905 size-full lazyloaded" data-lazy-sizes="(max-width: 114px) 100vw, 114px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-6.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-6.png 114w, https://ekuatio.com/wp-content/uploads/dominio-6-100x53.png 100w" data-was-processed="true" height="60" loading="lazy" sizes="(max-width: 114px) 100vw, 114px" src="https://ekuatio.com/wp-content/uploads/dominio-6.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-6.png 114w, https://ekuatio.com/wp-content/uploads/dominio-6-100x53.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="114" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Esta función existirá siempre, menos cuando el denominador sea igual a 0. Por tanto, debemos encontrar esa restricción que anula al denominador.</div>
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Para que exista la función, el denominador debe ser distinto de 0:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="cómo se calcula el dominio de una función racional" class="aligncenter wp-image-5904 size-full lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-7.png" data-was-processed="true" height="34" loading="lazy" src="https://ekuatio.com/wp-content/uploads/dominio-7.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="74" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Y esta restricción, es una ecuación de primer grado, de donde debemos despejar la x:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="dominio de una función" class="aligncenter wp-image-5903 size-full lazyloaded" data-lazy-sizes="(max-width: 166px) 100vw, 166px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-8.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-8.png 166w, https://ekuatio.com/wp-content/uploads/dominio-8-100x20.png 100w" data-was-processed="true" height="34" loading="lazy" sizes="(max-width: 166px) 100vw, 166px" src="https://ekuatio.com/wp-content/uploads/dominio-8.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-8.png 166w, https://ekuatio.com/wp-content/uploads/dominio-8-100x20.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="166" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Cuando x=1, el denominador será 0. Por tanto, para que exista f(x), x tiene que ser distinto de 1 y ese es el valor que hay que quitarle a R:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="dominio de funciones" class="aligncenter wp-image-5902 size-full lazyloaded" data-lazy-sizes="(max-width: 152px) 100vw, 152px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-9.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-9.png 152w, https://ekuatio.com/wp-content/uploads/dominio-9-150x28.png 150w, https://ekuatio.com/wp-content/uploads/dominio-9-100x18.png 100w" data-was-processed="true" height="28" loading="lazy" sizes="(max-width: 152px) 100vw, 152px" src="https://ekuatio.com/wp-content/uploads/dominio-9.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-9.png 152w, https://ekuatio.com/wp-content/uploads/dominio-9-150x28.png 150w, https://ekuatio.com/wp-content/uploads/dominio-9-100x18.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="152" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
El dominio es todo R menos el conjunto formado por el número 1.</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Vamos a ver otro ejemplo:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="como calcular dominio" class="aligncenter wp-image-5909 size-full lazyloaded" data-lazy-sizes="(max-width: 160px) 100vw, 160px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-10.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-10.png 160w, https://ekuatio.com/wp-content/uploads/dominio-10-100x41.png 100w" data-was-processed="true" height="65" loading="lazy" sizes="(max-width: 160px) 100vw, 160px" src="https://ekuatio.com/wp-content/uploads/dominio-10.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-10.png 160w, https://ekuatio.com/wp-content/uploads/dominio-10-100x41.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="160" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Igual que antes, esta función existirá siempre que el denominador no sea 0. Por tanto, calculamos los valores que hacen 0 el denominador:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="cálculo del dominio de una función" class="aligncenter wp-image-5910 size-full lazyloaded" data-lazy-sizes="(max-width: 211px) 100vw, 211px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-13.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-13.png 211w, https://ekuatio.com/wp-content/uploads/dominio-13-100x32.png 100w" data-was-processed="true" height="68" loading="lazy" sizes="(max-width: 211px) 100vw, 211px" src="https://ekuatio.com/wp-content/uploads/dominio-13.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-13.png 211w, https://ekuatio.com/wp-content/uploads/dominio-13-100x32.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="211" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Es decir, la función existirá siempre que x sea distinto de 2 y 3, por tanto el dominio es todo R menos 2 y 3:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="ejercicios de dominio de funciones" class="aligncenter wp-image-5907 size-full lazyloaded" data-lazy-sizes="(max-width: 169px) 100vw, 169px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-12.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-12.png 169w, https://ekuatio.com/wp-content/uploads/dominio-12-100x17.png 100w" data-was-processed="true" height="28" loading="lazy" sizes="(max-width: 169px) 100vw, 169px" src="https://ekuatio.com/wp-content/uploads/dominio-12.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-12.png 169w, https://ekuatio.com/wp-content/uploads/dominio-12-100x17.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="169" /></div>
<h3 style="background: rgb(255, 255, 255); border: 0px; color: #333333; font-family: Raleway, sans-serif; font-size: 1.387em; line-height: 1.5em; margin: 0px 0px 0.5em; outline: 0px; padding: 0px; vertical-align: baseline;">
<span id="Como_se_calcula_el_dominio_de_una_funcion_irracional" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Cómo se calcula el dominio de una función irracional</span></h3>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Las funciones irracionales son aquellas en las que aparece una raíz.</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Las de índice impar existen siempre.</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Las de índice par, existen siempre que su contenido sea igual o mayor que cero.</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Por ejemplo:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="como calcular dominio de una función" class="aligncenter wp-image-5916 size-full lazyloaded" data-lazy-sizes="(max-width: 128px) 100vw, 128px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-14.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-14.png 128w, https://ekuatio.com/wp-content/uploads/dominio-14-100x23.png 100w" data-was-processed="true" height="29" loading="lazy" sizes="(max-width: 128px) 100vw, 128px" src="https://ekuatio.com/wp-content/uploads/dominio-14.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-14.png 128w, https://ekuatio.com/wp-content/uploads/dominio-14-100x23.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="128" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Es una raíz de índice par, por tanto, existe siempre y cuando su contenido sea mayor o igual que 0:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="el dominio de una función" class="aligncenter wp-image-5915 size-full lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-15.png" data-was-processed="true" height="34" loading="lazy" src="https://ekuatio.com/wp-content/uploads/dominio-15.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="78" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
De esta inecuación, despejamos x y nos queda:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="cuál es el dominio de una función racional" class="aligncenter wp-image-5914 size-full lazyloaded" data-lazy-sizes="(max-width: 182px) 100vw, 182px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-16.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-16.png 182w, https://ekuatio.com/wp-content/uploads/dominio-16-100x19.png 100w" data-was-processed="true" height="34" loading="lazy" sizes="(max-width: 182px) 100vw, 182px" src="https://ekuatio.com/wp-content/uploads/dominio-16.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-16.png 182w, https://ekuatio.com/wp-content/uploads/dominio-16-100x19.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="182" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Por tanto, la función existirá siempre y cuando x sea mayor o igual que -2. Su dominio es:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="como determinar el dominio de una función" class="aligncenter wp-image-5913 size-full lazyloaded" data-lazy-sizes="(max-width: 159px) 100vw, 159px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-17.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-17.png 159w, https://ekuatio.com/wp-content/uploads/dominio-17-100x18.png 100w" data-was-processed="true" height="28" loading="lazy" sizes="(max-width: 159px) 100vw, 159px" src="https://ekuatio.com/wp-content/uploads/dominio-17.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-17.png 159w, https://ekuatio.com/wp-content/uploads/dominio-17-100x18.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="159" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Otro ejemplo:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="cual es el dominio de una función de primer grado" class="aligncenter wp-image-5912 size-full lazyloaded" data-lazy-sizes="(max-width: 138px) 100vw, 138px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-18.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-18.png 138w, https://ekuatio.com/wp-content/uploads/dominio-18-100x28.png 100w" data-was-processed="true" height="38" loading="lazy" sizes="(max-width: 138px) 100vw, 138px" src="https://ekuatio.com/wp-content/uploads/dominio-18.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-18.png 138w, https://ekuatio.com/wp-content/uploads/dominio-18-100x28.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="138" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Es una raíz de índice impar, luego existe siempre y su dominio es todo R:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="como hacer el dominio de una función" class="aligncenter wp-image-5911 size-full lazyloaded" data-lazy-sizes="(max-width: 107px) 100vw, 107px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-19.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-19.png 107w, https://ekuatio.com/wp-content/uploads/dominio-19-100x26.png 100w" data-was-processed="true" height="28" loading="lazy" sizes="(max-width: 107px) 100vw, 107px" src="https://ekuatio.com/wp-content/uploads/dominio-19.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-19.png 107w, https://ekuatio.com/wp-content/uploads/dominio-19-100x26.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="107" /></div>
<div class="adsb30" style="background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; margin: 12px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;">
</div>
<h3 style="background: rgb(255, 255, 255); border: 0px; color: #333333; font-family: Raleway, sans-serif; font-size: 1.387em; line-height: 1.5em; margin: 0px 0px 0.5em; outline: 0px; padding: 0px; vertical-align: baseline;">
<span id="Como_se_calcula_el_dominio_de_una_funcion_logaritmica" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Cómo se calcula el dominio de una función logarítmica</span></h3>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Las funciones logarítmicas con aquellas que la x está dentro de un logaritmo.</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Existen siempre y cuando el contenido del logaritmo no sea 0 o un número negativo, es decir, existirán siempre y cuando el contenido del logaritmo sea mayor que 0.</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Por ejemplo:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="dominio ejercicios resueltos" class="aligncenter wp-image-5920 size-full lazyloaded" data-lazy-sizes="(max-width: 163px) 100vw, 163px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-20.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-20.png 163w, https://ekuatio.com/wp-content/uploads/dominio-20-100x17.png 100w" data-was-processed="true" height="28" loading="lazy" sizes="(max-width: 163px) 100vw, 163px" src="https://ekuatio.com/wp-content/uploads/dominio-20.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-20.png 163w, https://ekuatio.com/wp-content/uploads/dominio-20-100x17.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="163" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Esta función existirá siempre que el contenido del logaritmo sea mayor que 0:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="como se halla el dominio de una función" class="aligncenter wp-image-5919 size-full lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-21.png" data-was-processed="true" height="27" loading="lazy" src="https://ekuatio.com/wp-content/uploads/dominio-21.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="69" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
De esta desigualdad, despejamos la x y nos queda:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="como hallar el dominio de una función ejercicios resueltos" class="aligncenter wp-image-5918 size-full lazyloaded" data-lazy-sizes="(max-width: 157px) 100vw, 157px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-22.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-22.png 157w, https://ekuatio.com/wp-content/uploads/dominio-22-100x22.png 100w" data-was-processed="true" height="34" loading="lazy" sizes="(max-width: 157px) 100vw, 157px" src="https://ekuatio.com/wp-content/uploads/dominio-22.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-22.png 157w, https://ekuatio.com/wp-content/uploads/dominio-22-100x22.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="157" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
La función existirá siempre que x sea mayor que 3. Por tanto su dominio será:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="cual es el dominio de una función polinomial" class="aligncenter wp-image-5921 size-full lazyloaded" data-lazy-sizes="(max-width: 145px) 100vw, 145px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-24.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-24.png 145w, https://ekuatio.com/wp-content/uploads/dominio-24-100x19.png 100w" data-was-processed="true" height="28" loading="lazy" sizes="(max-width: 145px) 100vw, 145px" src="https://ekuatio.com/wp-content/uploads/dominio-24.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-24.png 145w, https://ekuatio.com/wp-content/uploads/dominio-24-100x19.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="145" /></div>
<h3 style="background: rgb(255, 255, 255); border: 0px; color: #333333; font-family: Raleway, sans-serif; font-size: 1.387em; line-height: 1.5em; margin: 0px 0px 0.5em; outline: 0px; padding: 0px; vertical-align: baseline;">
<span id="Dominio_de_una_funcion_exponencial" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Dominio de una función exponencial</span></h3>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
Las funciones exponenciales son aquellas que tienen la x en el exponente, siendo la base:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-14003 lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/funciones-elementales-9.png" data-was-processed="true" height="29" loading="lazy" src="https://ekuatio.com/wp-content/uploads/funciones-elementales-9.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="82" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
Donde «a» es un número real mayor que 0 y distinto de 1:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-14004 lazyloaded" data-lazy-sizes="(max-width: 115px) 100vw, 115px" data-lazy-src="https://ekuatio.com/wp-content/uploads/funciones-elementales-10.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/funciones-elementales-10.png 115w, https://ekuatio.com/wp-content/uploads/funciones-elementales-10-100x30.png 100w" data-was-processed="true" height="34" loading="lazy" sizes="(max-width: 115px) 100vw, 115px" src="https://ekuatio.com/wp-content/uploads/funciones-elementales-10.png" srcset="https://ekuatio.com/wp-content/uploads/funciones-elementales-10.png 115w, https://ekuatio.com/wp-content/uploads/funciones-elementales-10-100x30.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="115" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
Podemos encontrarnos estas funciones como un número elevado a una función o también como el número e elevado a una función. Por ejemplo:</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-19611 lazyloaded" data-lazy-sizes="(max-width: 105px) 100vw, 105px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-27.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-27.png 105w, https://ekuatio.com/wp-content/uploads/dominio-27-72x100.png 72w" data-was-processed="true" height="146" loading="lazy" sizes="(max-width: 105px) 100vw, 105px" src="https://ekuatio.com/wp-content/uploads/dominio-27.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-27.png 105w, https://ekuatio.com/wp-content/uploads/dominio-27-72x100.png 72w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="105" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
En las funciones exponenciales no existe ningún valor de x que haga que la función no exista. Por tanto, f(x) existe siempre.</div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<b style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">El dominio de una función exponencial, es decir, un número elevado a una función o el número e elevado a una función, es todo el conjunto de los números reales:</b></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<img alt="dominio de una función" class="aligncenter wp-image-5906 size-full lazyloaded" data-lazy-sizes="(max-width: 107px) 100vw, 107px" data-lazy-src="https://ekuatio.com/wp-content/uploads/dominio-5.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/dominio-5.png 107w, https://ekuatio.com/wp-content/uploads/dominio-5-100x26.png 100w" data-was-processed="true" height="28" loading="lazy" sizes="(max-width: 107px) 100vw, 107px" src="https://ekuatio.com/wp-content/uploads/dominio-5.png" srcset="https://ekuatio.com/wp-content/uploads/dominio-5.png 107w, https://ekuatio.com/wp-content/uploads/dominio-5-100x26.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="107" /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<br /></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
Bueno, si habéis tenido la paciencia y e interés por haber llegado hasta aquí tengo que felicitaros y deciros que esa es la actitud que debéis de tener para poder llegar lejos en la vida y que todo el esfuerzo que estáis realizando os servirá de ayuda el próximo curso. Creo que os merecéis que hoy no os ponga otra tarea. El próximo día veremos algunos ejercicios de cálculo de dominios. Gracias.</div>
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Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-45320777840074974192020-05-14T09:54:00.002-07:002020-05-14T09:54:40.555-07:0015 MAYO 2020<br />
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<span style="font-family: "verdana" , sans-serif;">Buenos días, adjunto trabajo de repaso de sistemas, es recomendable, cuando se pueda, simplificar las ecuaciones del sistema antes de ponerse a resolverlo:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5VCHhVXudrIgWAIck8Md-qjfMrH8mj_v7PafVC7q3YGIBR7Xx8ybKRcpLf3r0ZLeAkBOP45f9rSO9-cQbhZfeOAOkP1lGb3n5RFDmaWP3zoQgKWeiHCcT9gPB_obrh6ChY8BjZyOusaY/s1600/sistemas.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="113" data-original-width="990" height="73" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5VCHhVXudrIgWAIck8Md-qjfMrH8mj_v7PafVC7q3YGIBR7Xx8ybKRcpLf3r0ZLeAkBOP45f9rSO9-cQbhZfeOAOkP1lGb3n5RFDmaWP3zoQgKWeiHCcT9gPB_obrh6ChY8BjZyOusaY/s640/sistemas.png" width="640" /></a></div>
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<span style="font-family: "verdana" , sans-serif;"><b>SOLUCIONES:</b></span></div>
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<span style="font-family: "verdana" , sans-serif;">Las soluciones son respectivamente:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLXYYjsSW2Ay4Zw3-QnMdIBxBedrHsEkycYaiPFYK7g1GOJpyS5vLeFvdJXEV4NrT6-jCOBpDbZAaBkvrfBxDVYNlI4W_C7clxxBG7Z44ptILxeNCxjk1kOXjG5f9EObDJ10Y964avKZM/s1600/soluciones.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="269" data-original-width="343" height="250" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLXYYjsSW2Ay4Zw3-QnMdIBxBedrHsEkycYaiPFYK7g1GOJpyS5vLeFvdJXEV4NrT6-jCOBpDbZAaBkvrfBxDVYNlI4W_C7clxxBG7Z44ptILxeNCxjk1kOXjG5f9EObDJ10Y964avKZM/s320/soluciones.png" width="320" /></a></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Buen finde.</span></div>
Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-6412794994586077992020-05-12T15:17:00.002-07:002020-05-12T15:17:54.694-07:0013 MAYO 2020<br />
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<span style="color: #274e13; font-family: Verdana, sans-serif;">Buenos días, hoy repasamos inecuaciones:</span><br />
<span style="color: #274e13; font-family: Verdana, sans-serif;"><br /></span>
<span style="color: #274e13; font-family: Verdana, sans-serif;">1 Resuelve la siguientes inecuaciones de primer grado y representa la solución en un recta <span style="font-size: x-small;"><i>(Recordamos se resuelven como una ecuación de primer grado hasta el momento de despejar la x, en ese momento si el coeficiente que acompaña a la x es positivo, se despeja normalmente y si es negativo cambiamos toda la inecuación de signo y la desigualdad de lado y después despejamos): </i></span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmWGcEu9lhqvGo14sryPmscUxpVGpACZUKmsdsBfRk9NKeKnu2056nsPnzJ3ihAsiLYgsguaKTTNfP7HdKRxD7_P13mqtbSxavxSlRNkkyFcHSpSZXf-OxdUhtwwSDP_hvTNvLJgZjLHPt/s1600/inecuacones+primer+grado.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="436" data-original-width="720" height="386" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmWGcEu9lhqvGo14sryPmscUxpVGpACZUKmsdsBfRk9NKeKnu2056nsPnzJ3ihAsiLYgsguaKTTNfP7HdKRxD7_P13mqtbSxavxSlRNkkyFcHSpSZXf-OxdUhtwwSDP_hvTNvLJgZjLHPt/s640/inecuacones+primer+grado.png" width="640" /></a></div>
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<span style="color: #274e13; font-family: Verdana, sans-serif;">2 Resuelve las siguientes inecuaciones de 2º grado<span style="font-size: x-small;"><i> (Si recordamos resolvemos la ecuación de segundo grado asociada, ponemos las soluciones en una recta y sustituimos un punto en cada intervalo en que nos queda dividida la recta y anotamos el signo + o - según corresponde. La solución que elegimos es la de los + si en la inecuación piden >0 o - si piden <0)</i></span>:</span></div>
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<span style="color: #274e13; font-family: Verdana, sans-serif;">3 Resuelve los siguientes sistemas de Inecuaciones<i><span style="font-size: x-small;"> (Si recordamos resolvemos las dos inecuaciones en la misma recta marcamos la solución de cada una con una línea y la solución del sistema es la parte donde hay doble línea)</span></i>:</span></div>
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Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-46661609206193252652020-05-10T16:20:00.000-07:002020-05-11T04:13:08.950-07:0011 MAY0 2020<br />
Buenos días chic@as hoy vamos a repasar un poco de trigonometría:<br />
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1. Calcula todas las RT de un ángulo del que sabemos <span style="background-color: white; color: #222222; font-family: "open sans" , "helvetica neue" , "helvetica" , "arial" , sans-serif; font-size: 16px;">que cos α = ¼ , y que 270º <α <360°</span><br />
<span style="background-color: white; color: #222222; font-family: "open sans" , "helvetica neue" , "helvetica" , "arial" , sans-serif; font-size: 16px;">2. Demuestra:</span><br />
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<img alt="Ejercicio sobre entidades trigonométricas equivalentes. 5" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-y-problemas-resueltos-de-trigonometria-6.gif" /></div>
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3. Halla "b" y "c" sabiendo que a=20 m:</div>
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<img alt="Triangulo ABC. 2" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-trigonometria-9.gif" /></div>
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4. <span style="background-color: white; color: #222222; font-family: "open sans" , "helvetica neue" , "helvetica" , "arial" , sans-serif; font-size: 16px;">Calcula la altura de un árbol, sabiendo que desde un punto </span><span style="background-color: white; color: #222222; font-family: "open sans" , "helvetica neue" , "helvetica" , "arial" , sans-serif; font-size: 16px;">del terreno se observa su copa bajo un ángulo de 30° y si nos </span><span style="background-color: white; color: #222222; font-family: "open sans" , "helvetica neue" , "helvetica" , "arial" , sans-serif; font-size: 16px;">acercamos 10 m, bajo un ángulo de 60°.</span></div>
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<img alt="Representaciones triangulares de los angulos" class="alignnone" src="https://www.superprof.es/apuntes/wp-content/uploads/2019/05/ejercicios-trigonometria-16.gif" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /></div>
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Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-12890266455363805362020-05-07T15:26:00.001-07:002020-05-10T15:36:45.461-07:008 MAYO 2020<br />
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Hoy solamente vamos a repasar ecuaciones (ojo con los menos, cuando son bicuadradas hacer el cambio de variable Z y después deshacerlo para hallar x, cuidado si aparecen los productos notables, en las que tienen raíces dejamos la raíz en un lado y todo lo demás en el otro y elevamos al cuadrado ambos lados de la igualdad y comprobamos ...), son obligatorias para todos!! : </span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjttx4M3cvf898tIm_JwfRV1KhfuEts2vj5ZzClkFJskTxBFPYN9gPzAPAmQX9l8m8TNLqk8j40kWNtgyxAihqwwI4HuHyi3HWb95ZuW6KFCx6Eq62eYdTGdtCRVoxnfQx9NPUCL5omRfw/s1600/pla.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #274e13; font-family: "verdana" , sans-serif;"><img border="0" data-original-height="232" data-original-width="1093" height="135" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjttx4M3cvf898tIm_JwfRV1KhfuEts2vj5ZzClkFJskTxBFPYN9gPzAPAmQX9l8m8TNLqk8j40kWNtgyxAihqwwI4HuHyi3HWb95ZuW6KFCx6Eq62eYdTGdtCRVoxnfQx9NPUCL5omRfw/s640/pla.png" width="640" /></span></a></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><b>Soluciones</b>: a) 2/3 y -1/2</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"> b) 1, -1, 5 y -5</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"> c) 1/10 y -1/2</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"> d) 2 y -1</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"> e) -1 y -4/15</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Antes de que me olvide, no es aconsejable copiar los ejercicios unos de otros, ni los que copian ni los que se dejan copiar, cada uno sabrá lo que hace, pero ...</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"> BUEN FINDE!</span></div>
Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-3854802728743477822020-05-05T15:29:00.001-07:002020-05-05T15:29:24.120-07:006 de MAYO 2020<span style="color: #274e13; font-family: Verdana, sans-serif;"><br /></span>
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<span style="color: #274e13; font-family: Verdana, sans-serif;">Vamos a seguir realizando ejercicios de repaso pero ahora vamos a hacerlo con ejercicios desde principio de curso. Los que tengáis suspensa la 1ª Evaluación deberéis de enviarme los ejercicios de radicales y polinomios al correo, pero aclaro que <i>en cualquier momento puedo pedirlos a cualquiera de vosotros</i> que deberéis de tenerlos hechos puesto que se tendrá en cuenta para vuestra calificación, son obligatorios. Son conceptos ya dados y nos sirven para afianzar lo aprendido, así que mucho ánimo y manos a la obra.</span><br />
<span style="color: #274e13; font-family: Verdana, sans-serif;">Como siempre cualquier duda al respecto la responderé en el mail.</span><br />
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<span style="color: #274e13; font-family: Verdana, sans-serif;"><b>OPERACIONES RADICALES</b></span><br />
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<span style="color: #274e13; font-family: Verdana, sans-serif;">SUMA DE RADICALES : Recordamos, descomponemos los radicandos en factores y extraemos fuera del radical todos los que estén elevados al grado de la raíz y finalmente sumamos los radicales iguales.</span><br />
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<span style="color: #274e13; font-family: Verdana, sans-serif;">PRODUCTO DE RADICALES: Pasamos los radicales al mismo índice y después ponemos una sola raíz y multiplicamos los radicandos</span><br />
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<span style="color: #274e13; font-family: Verdana, sans-serif;"><img alt="\displaystyle \sqrt{12} \cdot \sqrt[3]{36} =" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-d862bd7062e2dd5d747aa03221f2e59b_l3.png" /> </span></div>
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<span style="color: #274e13; font-family: Verdana, sans-serif;">RACIONALIZA: Recordamos que racionalizar es quitar la raíz del denominador, el ejercicio que os planteo es cuando el denominador había una suma o resta de raíces cuadradas en el que se multiplicaba y se dividía por el conjugado: </span><br />
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<span style="color: #274e13; font-family: Verdana, sans-serif;"> <img alt="\cfrac{2}{\sqrt{2}-\sqrt{3}}" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-bcb007f855b16b90dec6210329cdc2f9_l3.png" /></span></div>
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<span style="color: #274e13; font-family: Verdana, sans-serif;">FACTORIZACIÓN: Factoriza el siguiente polinomio e indica sus raíces:</span></div>
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<img alt="x^{4} - 10x^{2} + 9" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-cf1912887a010279eb70cc2753608155_l3.png" /></div>
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<span style="font-family: Verdana, sans-serif;"><span style="color: #274e13;">RECTAS:</span> <span style="color: #274e13;"><span style="background-color: white;">Hallar todas las ecuaciones de la recta que pasa por</span><span style="background-color: white;"> </span></span></span></div>
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<span style="color: #274e13; font-family: Verdana, sans-serif;"><span style="background-attachment: initial !important; background-clip: initial !important; background-image: none !important; background-origin: initial !important; background-position: initial !important; background-repeat: initial !important; background-size: initial !important; border-color: initial !important; border-image: initial !important; border-width: initial !important; box-sizing: inherit; height: auto;"><img alt=" A(1,3)" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-c0bc0443bf01a2e72f4ed1aa3e4d6466_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -6px;" title="Rendered by QuickLaTeX.com" /></span> y <img alt=" B(2,-5)" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-d7a8feed1f25a3396b5076a375f47e23_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -6px;" title="Rendered by QuickLaTeX.com" /></span></div>
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<br />Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-87128649526878936372020-05-03T14:46:00.002-07:002020-05-04T02:04:58.788-07:004 MAYO 2020<br />
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Hola chic@s, seguimos repasando vectores y rectas. Os planteo unos ejercicios de repaso con soluciones para que hagáis en vuestro cuaderno.</span><br />
<span style="color: #274e13; font-family: "verdana" , sans-serif;"><br /></span><span style="color: #274e13; font-family: "verdana" , sans-serif;"><br /></span><span style="color: #274e13; font-family: "verdana" , sans-serif;"><b>EJERCICIO 1</b> : Halla el punto medio del segmento de extremos P(2, 1) y Q(-4, 3). </span><br />
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><b>SOL</b>: M(-1, 2) </span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><b>EJERCICIO 2</b> : Determinar si los puntos A(3,1), B(5,2) y C(1,0) están alineados. </span><br />
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><b>SOL:</b> Sí </span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><b>EJERCICIO 3 </b>: Escribe la ecuación general de la recta, r, que pasa por los puntos (1, 0) y (3, 6).</span><br />
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><b>SOL:</b> 3x - y -3 = 0</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><b>EJERCICIO 4:</b> Halla la ecuación explícita de la recta, r, que pasa por (3, 2) y tiene como vector dirección v(1,1).</span><br />
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><b>SOL:</b> y = x - 1 </span></div>
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<b style="color: #274e13; font-family: verdana, sans-serif;">EJERCICIO 5: </b><span style="color: #274e13; font-family: "verdana" , sans-serif;">Obtén la ecuación general de la recta, , que pasa por (3, 1) y tiene pendiente m=-1/2 . </span></div>
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<b style="color: #274e13; font-family: verdana, sans-serif;">SOL: </b><span style="color: #274e13; font-family: "verdana" , sans-serif;"> x+2y-5=0 </span></div>
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Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-29537831045684824342020-04-28T15:21:00.003-07:002020-04-29T03:58:16.736-07:0030 ABRIL 2020<h3 style="background: rgb(255, 255, 255); border: 0px; font-family: raleway, sans-serif; font-size: 1.387em; line-height: 1.5em; margin: 0px 0px 0.5em; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
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<span style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13;">Gracias chic@s por vuestro trabajo y no bajéis la guardia pese a las circunstancias. Hoy os planteo tres ejercicios, como siempre después pondré las soluciones pero recordad que es importante intentarlo porque sabéis, sois inteligentes, podéis ... y tener siempre presente que "toda dificultad es una superación de vosotros mismos"</span></span></h3>
<div>
<span style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13;"><br /></span></span></div>
<h3 style="background: rgb(255, 255, 255); border: 0px; font-family: Raleway, sans-serif; font-size: 1.387em; line-height: 1.5em; margin: 0px 0px 0.5em; outline: 0px; padding: 0px; vertical-align: baseline;">
<span id="Ejercicio_1" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13;">Ejercicio 1</span></span></h3>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13;">Dada la recta de ecuación 2x-3y+6=0, escríbela en forma contínua, paramétrica, vectorial y explícita.</span></strong></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13;"><br /></span></strong></div>
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<span id="Ejercicio_2" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13;">Ejercicio 2</span></span></h3>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<span style="color: #274e13;"><strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></strong></span></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13;">El punto P (3,1), ¿pertenece a la recta que pasa por el punto A (-2,-2) y tiene como vector director v=(1,3)?</span></strong></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13;"><br /></span></strong></div>
<h3 style="background: rgb(255, 255, 255); border: 0px; font-family: Raleway, sans-serif; font-size: 1.387em; line-height: 1.5em; margin: 0px 0px 0.5em; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
<span id="Ejercicio_3" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13;">Ejercicio 3</span></span></h3>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13;">Determina la ecuación de las rectas siguientes y expresa en forma implícita y explicita:</span></strong></div>
<div style="-webkit-hyphenate-character: "‐"; background: rgb(255, 255, 255); border: 0px; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline; widows: 3;">
<strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13;">a: la recta que corta los ejes de coordenadas en los puntos C(0,-1) D(3,0)</span></strong></div>
<div style="background: rgb(255, 255, 255); border: 0px; font-family: raleway, sans-serif; font-stretch: normal; line-height: 1.618; margin-bottom: 1.618em; outline: 0px; padding: 0px; text-align: justify; vertical-align: baseline;">
<div style="font-size: 14px;">
<strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13;">b: la recta que pasa por el punto A(1,-2) y tiene pendiente m=-2</span></strong></div>
<div style="font-size: 14px;">
<strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="color: #274e13;"><br /></span></strong></div>
<h2 style="text-align: center;">
<span style="color: #274e13; font-size: large;">SOLUCIONES</span></h2>
<div>
<h3 style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #333333; font-family: Raleway, sans-serif; font-size: 1.387em; line-height: 1.5em; margin: 0px 0px 0.5em; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline;">
<span id="Ejercicio_1" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">SOL 1</span></h3>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
<strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Dada la recta de ecuación 2x-3y+6=0, escríbela en forma contínua, paramétrica, vectorial y explícita.</strong></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Tenemos la siguiente recta:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11815 lazyloaded" data-lazy-sizes="(max-width: 117px) 100vw, 117px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-105.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-105.png 117w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-105-100x23.png 100w" data-was-processed="true" height="27" loading="lazy" sizes="(max-width: 117px) 100vw, 117px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-105.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-105.png 117w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-105-100x23.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="117" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
Necesitamos obtener el vector de dirección y un punto que pertenece a la recta. Con estos dos datos, podemos obtener la ecuación vectorial, la paramétrica y la contínua.</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Cuando la recta está en forma genera Ax+By+C=0 el vector director es v(-B, A). Entonces en nuestrocaso el vector de dirección es:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11816 lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-106.png" data-was-processed="true" height="42" loading="lazy" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-106.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="98" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
Para obtener un punto de la recta, le damos a x el valor que queramos, por ejemplo x=0 y despejamos el valor de «y»:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11817 lazyloaded" data-lazy-sizes="(max-width: 329px) 100vw, 329px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-107.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-107.png 329w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-107-300x31.png 300w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-107-100x10.png 100w" data-was-processed="true" height="34" loading="lazy" sizes="(max-width: 329px) 100vw, 329px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-107.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-107.png 329w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-107-300x31.png 300w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-107-100x10.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="329" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Por lo que el punto que pertenece a la recta es:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11818 lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-108.png" data-was-processed="true" height="28" loading="lazy" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-108.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="79" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Con este punto y el vector de dirección obtenemos la <strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><a href="https://ekuatio.com/lesson/4-ecuaciones-vectorial-y-parametricas-de-la-recta-ejercicios-resueltos/" style="background: transparent; border: 0px; color: #7088b7; margin: 0px; outline: 0px; padding: 0px; text-decoration-line: none; vertical-align: baseline;">ecuación vectorial</a></strong>:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11819 lazyloaded" data-lazy-sizes="(max-width: 179px) 100vw, 179px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-109.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-109.png 179w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-109-100x15.png 100w" data-was-processed="true" height="27" loading="lazy" sizes="(max-width: 179px) 100vw, 179px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-109.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-109.png 179w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-109-100x15.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="179" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Las <a href="https://ekuatio.com/lesson/4-ecuaciones-vectorial-y-parametricas-de-la-recta-ejercicios-resueltos/" style="background: transparent; border: 0px; color: #7088b7; margin: 0px; outline: 0px; padding: 0px; text-decoration-line: none; vertical-align: baseline;"><strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">ecuaciones paramétricas</strong></a>:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11820 lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-110.png" data-was-processed="true" height="83" loading="lazy" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-110.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="98" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<span style="color: #555555;">Y la</span> <span style="color: #0b5394;"><b>ecuación contínua</b><b>:</b></span></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11821 lazyloaded" data-lazy-sizes="(max-width: 129px) 100vw, 129px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-111.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-111.png 129w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-111-100x47.png 100w" data-was-processed="true" height="60" loading="lazy" sizes="(max-width: 129px) 100vw, 129px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-111.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-111.png 129w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-111-100x47.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="129" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
La ecuación explícita la vamos a obtener a partir de la general </div>
<span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border-image: initial; border-radius: 0.237em; font-size: 14px; height: auto; margin-bottom: 1.414em; margin-left: auto; margin-right: auto; outline-color: initial; outline-style: initial; padding: 0.327em;"><img alt="" class="aligncenter size-full wp-image-11815 lazyloaded" data-lazy-sizes="(max-width: 117px) 100vw, 117px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-105.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-105.png 117w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-105-100x23.png 100w" data-was-processed="true" height="27" loading="lazy" sizes="(max-width: 117px) 100vw, 117px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-105.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-105.png 117w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-105-100x23.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; color: #555555; display: block; font-family: Raleway, sans-serif; height: auto; margin: 0px auto 1.414em; max-width: 100%; orphans: 3; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom; widows: 3;" width="117" /></span><br />
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
despejando la "y", entonces </div>
<span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border-image: initial; border-radius: 0.237em; font-size: 14px; height: auto; margin-bottom: 1.414em; margin-left: auto; margin-right: auto; outline-color: initial; outline-style: initial; padding: 0.327em;"><img alt="" class="aligncenter size-full wp-image-11824 lazyloaded" data-lazy-sizes="(max-width: 102px) 100vw, 102px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-114.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-114.png 102w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-114-100x59.png 100w" data-was-processed="true" height="60" loading="lazy" sizes="(max-width: 102px) 100vw, 102px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-114.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-114.png 102w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-114-100x59.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; color: #555555; display: block; font-family: Raleway, sans-serif; height: auto; margin: 0px auto 1.414em; max-width: 100%; orphans: 3; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom; widows: 3;" width="102" /></span><br />
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Finalmente, separamos la fracción en dos términos para que se quede en forma <a href="https://ekuatio.com/lesson/6-ecuacion-punto-pendiente-y-explicita-de-la-recta-pendiente-de-una-recta/" style="background: transparent; border: 0px; color: #7088b7; margin: 0px; outline: 0px; padding: 0px; text-decoration-line: none; vertical-align: baseline;"><strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">explícita</strong></a>:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11825 lazyloaded" data-lazy-sizes="(max-width: 103px) 100vw, 103px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-115.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-115.png 103w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-115-100x58.png 100w" data-was-processed="true" height="60" loading="lazy" sizes="(max-width: 103px) 100vw, 103px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-115.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-115.png 103w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-115-100x58.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="103" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<br /></div>
<h3 style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #333333; font-family: Raleway, sans-serif; font-size: 1.387em; line-height: 1.5em; margin: 0px 0px 0.5em; outline: 0px; padding: 0px; vertical-align: baseline;">
<span id="Ejercicio_2" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Sol 2</span></h3>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
<strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">El punto P (3,1), ¿pertenece a la recta que pasa por el punto A (-2,-2) y tiene como vector director v=(1,3)?</strong></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
Para saber si el punto pertenece a la recta, vamos a calcular la ecuación contínua y después sustituiremos las coordenadas del punto por la x y por la «y» en la recta y veremos si se cumple al igualdad.</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Entonces, tenemos el punto y el vector de dirección:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11709 lazyloaded" data-lazy-sizes="(max-width: 101px) 100vw, 101px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-1.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-1.png 101w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-1-100x99.png 100w" data-was-processed="true" height="100" loading="lazy" sizes="(max-width: 101px) 100vw, 101px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-1.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-1.png 101w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-1-100x99.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="101" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
En la ecuación contínua:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11710 lazyloaded" data-lazy-sizes="(max-width: 145px) 100vw, 145px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-2.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-2.png 145w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-2-100x43.png 100w" data-was-processed="true" height="63" loading="lazy" sizes="(max-width: 145px) 100vw, 145px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-2.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-2.png 145w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-2-100x43.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="145" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<span style="font-size: 14px;">Sustituimos X</span><span style="font-size: xx-small;">0</span><span style="font-size: 14px;"> e Y</span><span style="font-size: xx-small;">0</span><span style="font-size: 14px;"> por las coordenadas del punto, y a y b por las coordenadas del vector de dirección:</span></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11712 lazyloaded" data-lazy-sizes="(max-width: 137px) 100vw, 137px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-4.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-4.png 137w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-4-100x44.png 100w" data-was-processed="true" height="60" loading="lazy" sizes="(max-width: 137px) 100vw, 137px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-4.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-4.png 137w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-4-100x44.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="137" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Ya tenemos la ecuación contínua.</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Ahora, vamos a ver si el punto P (3,1) pertenece a esa recta, y para eso tiene que cumplir la ecuación:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Sustituimos sus coordenadas por x y por «y»:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11714 lazyloaded" data-lazy-sizes="(max-width: 139px) 100vw, 139px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-6.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-6.png 139w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-6-100x43.png 100w" data-was-processed="true" height="60" loading="lazy" sizes="(max-width: 139px) 100vw, 139px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-6.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-6.png 139w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-6-100x43.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="139" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Operamos en ambos miembros y vemos que no se cumple la igualdad:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11715 lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-7.png" data-was-processed="true" height="34" loading="lazy" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-7.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="53" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Por tanto, el punto P (3,1) <b>no</b> pertenece a la recta</div>
<div class="adsb30" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; margin: 12px; outline: 0px; padding: 0px; text-align: center; vertical-align: baseline;">
</div>
<h3 style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #333333; font-family: Raleway, sans-serif; font-size: 1.387em; line-height: 1.5em; margin: 0px 0px 0.5em; outline: 0px; padding: 0px; vertical-align: baseline;">
<span id="Ejercicio_3" style="background: transparent; border: 0px; font-size: 19.418px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Sol 3</span></h3>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
<strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Determina la ecuación de las rectas siguientes y expresa en forma implícita y explicita:</strong></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
<strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">a: la recta que corta los ejes de coordenadas en los puntos C(0,-1) D(3,0)</strong></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
<span style="text-align: start;">Tenemos los puntos:</span></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11716 lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-8.png" data-was-processed="true" height="86" loading="lazy" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-8.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="92" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Necesitamos un punto y un vector. Como punto nos vale cualquiera de los dos por ejemplo C(0, -1) y como vector el CD=D-C=(3, 1). Entonces hallamos la ecuación continua:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11719 lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-11.png" data-was-processed="true" height="60" loading="lazy" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-11.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="93" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<span style="color: #555555;">Para obtener la </span><span style="color: #3d85c6;"><b>ecuación implícta</b></span><span style="color: #555555;"> multiplicamos en cruz y pasamos todos los términos para un lado de la igualdad:</span></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11722 lazyloaded" data-lazy-sizes="(max-width: 102px) 100vw, 102px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-14.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-14.png 102w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-14-100x26.png 100w" data-was-processed="true" height="27" loading="lazy" sizes="(max-width: 102px) 100vw, 102px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-14.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-14.png 102w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-14-100x26.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="102" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<span style="color: #555555;">Para obtener la </span><span style="color: #3d85c6;"><b>ecuación explícita</b></span><span style="color: #555555;">, despejamos la «y»:</span></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11723 lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-15.png" data-was-processed="true" height="60" loading="lazy" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-15.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="87" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Y separamos en dos términos, uno con x y otro sin x:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11724 lazyloaded" data-lazy-sizes="(max-width: 119px) 100vw, 119px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-16.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-16.png 119w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-16-100x50.png 100w" data-was-processed="true" height="60" loading="lazy" sizes="(max-width: 119px) 100vw, 119px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-16.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-16.png 119w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-16-100x50.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="119" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Y simplificamos el segundo término:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11725 lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-17.png" data-was-processed="true" height="60" loading="lazy" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-17.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="99" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; vertical-align: baseline; widows: 3;">
<strong style="background: transparent; border: 0px; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">b: la recta que pasa por el punto A(1,-2) y tiene pendiente m=-2</strong></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Tenemos un punto y la pendiente:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11726 lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-18.png" data-was-processed="true" height="84" loading="lazy" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-18.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="91" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Calcularemos la ecuación de la recta con la ecuación punto pendiente:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11727 lazyloaded" data-lazy-sizes="(max-width: 145px) 100vw, 145px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-19.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-19.png 145w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-19-100x20.png 100w" data-was-processed="true" height="29" loading="lazy" sizes="(max-width: 145px) 100vw, 145px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-19.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-19.png 145w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-19-100x20.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="145" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<span style="font-size: 14px;">Sustituimos X</span><span style="font-size: xx-small;">0</span><span style="font-size: 14px;"> e Y</span><span style="font-size: xx-small;">0</span><span style="font-size: 14px;"> por las coordenadas del punto y m por su valor:</span></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11728 lazyloaded" data-lazy-sizes="(max-width: 150px) 100vw, 150px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-20.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-20.png 150w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-20-100x18.png 100w" data-was-processed="true" height="27" loading="lazy" sizes="(max-width: 150px) 100vw, 150px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-20.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-20.png 150w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-20-100x18.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="150" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
Operamos:</div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11729 lazyloaded" data-lazy-sizes="(max-width: 106px) 100vw, 106px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-21.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-21.png 106w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-21-100x25.png 100w" data-was-processed="true" height="27" loading="lazy" sizes="(max-width: 106px) 100vw, 106px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-21.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-21.png 106w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-21-100x25.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="106" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<span style="color: #555555;">La </span><span style="color: #3d85c6;"><b>ecuación implícita</b></span><span style="color: #555555;"> la obtenemos pasando todos los términos al primer miembro y reordenando:</span></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11730 lazyloaded" data-lazy-sizes="(max-width: 102px) 100vw, 102px" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-22.png" data-lazy-srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-22.png 102w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-22-100x26.png 100w" data-was-processed="true" height="27" loading="lazy" sizes="(max-width: 102px) 100vw, 102px" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-22.png" srcset="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-22.png 102w, https://ekuatio.com/wp-content/uploads/ejercicios-rectas-22-100x26.png 100w" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="102" /></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<span style="color: #555555;">Y la </span><b><span style="color: #3d85c6;">ecuación explícita</span></b><span style="color: #555555;"> despejando «y»:</span></div>
<div style="-webkit-hyphenate-character: "‐"; background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; color: #555555; font-family: Raleway, sans-serif; font-size: 14px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.618; margin-bottom: 1.618em; orphans: 3; outline: 0px; padding: 0px; text-align: start; vertical-align: baseline; widows: 3;">
<img alt="" class="aligncenter size-full wp-image-11731 lazyloaded" data-lazy-src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-23.png" data-was-processed="true" height="27" loading="lazy" src="https://ekuatio.com/wp-content/uploads/ejercicios-rectas-23.png" style="background: rgba(255, 255, 255, 0.7); border-radius: 0.237em; border: 2px solid rgb(238, 238, 238); box-sizing: border-box; display: block; height: auto; margin: 0px auto 1.414em; max-width: 100%; outline: 0px; padding: 0.327em; text-align: center; vertical-align: bottom;" width="83" /></div>
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Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-38683372530918143372020-04-26T15:08:00.000-07:002020-04-26T15:08:03.663-07:0027 ABRIL 2020<div style="text-align: justify;">
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Nueva semana chic@s, algunos váis un poco atrasados así que os recomiendo que no os relajéis, poco a poco pero siguiendo una rutina, es la mejor manera de que no se acumule el trabajo. Seguid el consejo y mucho ánimo.</span></span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><i><b>Los ejercicios que hoy os planteo son para entregar</b></i>, pero para saber hacerlos tenéis que haber hecho los que puse en todas las entradas después de Semana Santa, <b><i>así que esos también los quiero ver. Es decir quiero ver todos los ejercicios desde semana santa. (fecha límite sábado)</i></b></span><br />
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Son similares a los que estamos haciendo (puse dos de rectas y dos de vectores) así que si tenéis alguna duda podéis revisar las entradas anteriores.</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Respecto de los que me habéis entregado os he contestado a los que los teníais regular o mal, a los que los tenías bien o muy bien ya no os dije nada así que daros ahora por enterados y enhorabuena. Los que lo teníais regular revisar los fallos que os comenté y podéis consultar las soluciones que ya colgué en la entrada del día <i><b>MIÉRCOLES 1/04/2020</b></i>.</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><b>EJERCICIO 1:</b> </span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"> Hallar todas las ecuaciones de la recta que pasa por el punto A(-1, 3) y tiene como vector director v(2, -3).</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><b>EJERCICIO 2:</b></span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"> Hallar todas las ecuaciones de la recta que pasa por los puntos A(2, -1) y B(3, 5).</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"> Halla el ángulo que forman los vectores u(1, 1) y v(-3, 3).</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><b>EJERCICIO 4:</b></span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"> Comprobar si los puntos A(1,1), B(0, -1) y C(5,10) están alineados utilizando vectores.</span></div>
<span style="color: #274e13; font-family: "verdana" , sans-serif;"><br /></span><span style="color: #274e13; font-family: "verdana" , sans-serif;"><br /></span>Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-24056161815275012020-04-23T07:44:00.000-07:002020-04-27T03:01:17.882-07:0024 ABRIL 2020<span style="color: #274e13; font-family: "verdana" , sans-serif;"><br /></span>
<span style="color: #274e13; font-family: "verdana" , sans-serif;">Hola chic@s, hoy vamos a terminar con las ecuaciones de la recta. El lunes haremos un ejercicio pasando de una a otra ecuación, recordar que todas son equivalentes.</span><br />
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><br /></span><span style="color: #274e13; font-family: "verdana" , sans-serif;">Ecuación general o implícita</span></h2>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Fijaros que lo que tenemos que hacer es partiendo de la ecuación contínua que vimos ayer igualamos multiplicando en cruz y pasamos todo para el otro lado de la igualdad.</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Ecuación explícita</span></h2>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Ecuación punto-pendiente</span></h2>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><span style="color: #274e13; font-family: "verdana" , sans-serif;"> <b> </b></span><b><span style="color: #274e13; font-family: "verdana" , sans-serif;"> La ecuación punto pendiente es </span><img alt="y-y_0= m(x-x_0)" height="42" src="https://matematicasies.com/local/cache-vignettes/L170xH42/42997d19e7fb4a24f1c8be639676f799-b97f1.png?1572666089" style="background-color: white; border: 0px; font-size: 15.0015px; height: auto; max-width: 100%; vertical-align: middle;" title="y-y_0= m(x-x_0)" width="170" /> siendo m la pendiente y P(x<span style="font-size: xx-small;">o</span>,y<span style="font-size: xx-small;">o</span>) un punto de la recta. La pendiente se halla dividiendo la segunda coordenada del vector entre la primera, es decir, m=v<span style="font-size: xx-small;">2</span>/v<span style="font-size: xx-small;">1</span></b></span><br />
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<span style="color: #274e13;"><span style="font-family: "verdana" , sans-serif;">Ejemplo:</span><span style="font-family: "verdana" , sans-serif;"><span style="background-color: white;">Tenemos una recta pasa por el punto</span><span style="background-color: white;"> </span><img align="absmiddle" alt="menos 1, 3" class="alignnone" src="https://latex.codecogs.com/gif.latex?A(-1,&space;3)" style="background-color: white; background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /><span style="background-color: white;"> y tiene un vector director</span><span style="background-color: white;"> </span><img align="absmiddle" alt="2, 5" class="alignnone" src="https://latex.codecogs.com/gif.latex?\vec{v}&space;=&space;(2,&space;5)" style="background-color: white; background-repeat: no-repeat; border-style: none; box-sizing: inherit; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /><span style="background-color: white;">. Escribe su ecuación punto-pendiente.</span></span></span><br />
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<span style="color: #274e13;"><span style="font-family: "verdana" , sans-serif;"> </span><em style="background-repeat: no-repeat; box-sizing: inherit; font-family: Verdana, sans-serif; margin: 0px; padding: 0px;">Solución</em><span style="font-family: "verdana" , sans-serif;">: Se nos proporcionó un vector director</span><span style="font-family: "verdana" , sans-serif;"> </span><img align="absmiddle" alt="v" src="https://latex.codecogs.com/gif.latex?\vec{v}" style="background-repeat: no-repeat; border-style: none; box-sizing: inherit; font-family: Verdana, sans-serif; height: auto; margin: 0px; max-width: 100%; padding: 0px;" /><span style="font-family: "verdana" , sans-serif;">, por lo que su pendiente está dada por</span></span></div>
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<span style="color: #274e13;"><span style="font-family: "verdana" , sans-serif;"> </span><img alt="\displaystyle m = \frac{v_2}{v_1} = \frac{5}{2}" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-dd1fc12e01693c4c6ad5bfc3e0cf2d1b_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; font-family: Verdana, sans-serif; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; text-align: center; vertical-align: -19px;" title="Rendered by QuickLaTeX.com" /></span></div>
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<span style="color: #274e13;"><span style="font-family: "verdana" , sans-serif;"> </span><span style="font-family: "verdana" , sans-serif;">De esta manera, sustituyendo en la ecuación punto-pendiente con</span><span style="font-family: "verdana" , sans-serif;"> </span><span style="font-family: "verdana" , sans-serif;">x</span><span style="font-family: "verdana" , sans-serif; font-size: xx-small;">o</span><span style="font-family: "verdana" , sans-serif;">=-1 e </span><span style="font-family: "verdana" , sans-serif;">y</span><span style="font-family: "verdana" , sans-serif; font-size: xx-small;">o</span><span style="font-family: "verdana" , sans-serif;"> =3 </span><span style="font-family: "verdana" , sans-serif;">, tenemos que</span></span></div>
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<span style="color: #274e13;"> <img alt="{ \displaystyle y - 3 = \frac{5}{2}(x + 1) }" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-4d771e021fc8358a1947d415c0157251_l3.png" style="background: none !important; border: none !important; box-sizing: inherit; font-size: 1.6rem; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; text-align: center; vertical-align: -14px;" title="Rendered by QuickLaTeX.com" /></span></div>
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<b><span style="color: #274e13;">EJERCICIOS</span></b></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><i><b>Ejercicio 1:</b> Halla la ecuación general, la explícita y la punto pendiente de la recta que pasa por P((2, -3) y tiene como vector v(2, 1).</i></span></div>
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<i><b style="color: #274e13; font-family: Verdana, sans-serif;">Ejercicio 2:</b><span style="color: #274e13; font-family: "verdana" , sans-serif;"> </span><span style="color: #274e13; font-family: "verdana" , sans-serif;">Halla la ecuación general, la explícita y la punto pendiente de la recta que pasa por A(-3,0) y B(5,-2)</span></i><br />
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Bueno con esto terminamos la clase de hoy, en breve colgaré las soluciones, buen finde y mucho ánimo.</span><br />
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">SOLUCIONES</span></h2>
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Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-9127479585647798262020-04-21T15:12:00.001-07:002020-04-23T07:01:58.510-07:0022 ABRIL 2020<br />
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<span style="font-family: "verdana" , sans-serif;">Hola chic@s hoy vamos a trabajar con las ecuaciones de la recta en forma paramétrica y en forma continua:</span></div>
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<span style="font-family: "verdana" , sans-serif;"><b>Ecuaciones paramétricas:</b></span></h2>
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<span style="font-family: "verdana" , sans-serif;"><b>Ecuación continua:</b></span></h2>
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<span style="font-family: "verdana" , sans-serif;"><b>EJERCICIO 1:</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="background-color: white; color: #222222; font-size: 16px;">Una recta pasa por el punto </span><span class="escarlata" style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; font-size: 16px; margin: 0px; padding: 0px;">A</span><span style="background-color: white; color: #222222; font-size: 16px;">(-1, 3) y tiene un vector director </span><img alt="\vec{v} = (2,5)" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-4b57693d832011ec1e54fdb84163f243_l3.png" style="background-color: white; background-image: none; border: none; box-sizing: inherit; color: #222222; font-size: 16px; height: auto; margin: 0px; max-width: 100%; padding: 0px; vertical-align: -6px;" title="Rendered by QuickLaTeX.com" /><span style="background-color: white; color: #222222; font-size: 16px;">. escribir sus ecuaciones paramétrica y continua.</span></span></div>
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<b style="font-family: Verdana, sans-serif;">EJERCICIO 2:</b></div>
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<span style="font-family: "verdana" , sans-serif;">Hallar las ecuaciones </span><span style="background-color: white; color: #222222; font-family: "verdana" , sans-serif; font-size: 16px;">paramétrica y continua </span><span style="font-family: "verdana" , sans-serif;">de la recta que pasa por los puntos A(-2,1) y B(3,4).</span></div>
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<b style="font-family: Verdana, sans-serif;">EJERCICIO 3:</b></div>
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<span style="font-family: "verdana" , sans-serif;">Indica un punto y un vector de las siguientes rectas:</span></div>
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<span style="font-family: "verdana" , sans-serif;"> a) </span><img src="https://ekuatio.com/wp-content/uploads/ecuaciones-vectorial-y-param%C3%A9trica-24.png" /> b)<img src="https://www.ematematicas.net/cgi-bin/mimetex.cgi?\;\frac{x\;-\;3}{1}\;=\;\;\frac{y\;-\;1}{2}" /></div>
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<span style="font-family: Verdana, sans-serif; font-size: large;"><b>SOLUCIONES</b></span></div>
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Tomáshttp://www.blogger.com/profile/17371543730330838095noreply@blogger.com0tag:blogger.com,1999:blog-2896795997799832059.post-1859475982948667692020-04-19T15:43:00.003-07:002020-04-20T07:42:39.110-07:0020 ABRIL 2020<div style="background-color: white; margin-bottom: 1.46667em; text-align: justify;">
<span style="color: #274e13; font-family: "verdana" , sans-serif;">Hola chic@s vamos a avanzar un poco y empezar con el tema de rectas en el plano. Como siempre mucho ánimo y recordar que podéis porque sois muy inteligentes.</span><br />
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">ECUACIONES DE LA RECTA</span></h2>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Primeramente aclararemos algunos conceptos:</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">¿qué es una recta y que es el plano?</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Si pensamos en el plano de manera analítica, es decir, pensando en puntos, diríamos que está formado por todos los pares (x,y) donde x e y son números reales, es decir, el plano está formado por todas las combinaciones posibles (x,y). Si dibujamos unos ejes cartesianos o ejes de cooredenadas y pudiéramos pintar todas las posibilidades de pares (x,y) llenaríamos el plano. </span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Si pensamos ahora en una recta dentro del plano diríamos que es un subconjunto de los puntos del plano que están alineados. Es decir, de todos los puntos del plano son los que cumplen una condición.</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">¿Que es la ecuación de una recta?</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><span style="font-style: normal; font-weight: 400;">Entonces para que estando en un plano nos quedemos sólo con los puntos de una recta tenemos que ponerle condiciones a esos puntos (x,y), eso serán las ecuaciones de la recta, o sea,</span><b> <i>las ecuaciones de una recta son las condiciones que le imponemos a los puntos del plano para determinar dicha recta.</i></b></span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Veamos entonces las ecuaciones de la recta:</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Si pensamos en un punto del plano <b>P</b><b><span style="font-size: xx-small;">o</span></b> y en una dirección <b>v</b>, existe una única recta que pasa por ese punto y tenga esa dirección. Si dibujáis en la libreta un punto y en ese punto una flecha (que sería el vector) podríais trazar una única recta.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPqjoh82yW-OSrL4xJhRxou1r8e_tj1uN2W47kUxdtkowDs3sYOmXeGweUx_2gt_8KqIrg90xBpgqOXiI5DYMtmIIg9g28WyNiTr5aFKeKvNrRL_jDs1gAzlI9n7os35eEXCQ7MFZafUHU/s1600/recta.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #274e13; font-family: "verdana" , sans-serif;"><img border="0" data-original-height="245" data-original-width="366" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPqjoh82yW-OSrL4xJhRxou1r8e_tj1uN2W47kUxdtkowDs3sYOmXeGweUx_2gt_8KqIrg90xBpgqOXiI5DYMtmIIg9g28WyNiTr5aFKeKvNrRL_jDs1gAzlI9n7os35eEXCQ7MFZafUHU/s320/recta.png" width="320" /></span></a></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">es decir, <i><b>con un punto y una dirección o vector queda determinada de manera unívoca una recta. </b></i></span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><span style="background-color: white;">Veam</span><span style="background-color: white;">os un resumen de todas las ecuaciones de la recta que</span></span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> pasa por el punto <span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt=" (x_0,y_0 )" height="42" src="https://matematicasies.com/local/cache-vignettes/L63xH42/7cbcedc73ee64e0c384b49c4cfaf6ba1-883bb.png?1572607125" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title=" (x_0,y_0 )" width="63" /></span></span></div>
<span style="color: #274e13; font-family: "verdana" , sans-serif;"><span style="border-color: initial; border-image: initial; border-style: initial; height: auto;"><img alt="-" class="puce" height="11" src="https://matematicasies.com/local/cache-vignettes/L8xH11/puce-32883.gif?1572598111" style="border: 0px; height: auto; max-width: 100%; vertical-align: baseline;" width="8" /></span> tiene como vector director <img alt="\vec{v}=(v_1,v_2)" height="42" src="https://matematicasies.com/local/cache-vignettes/L100xH42/e0d202189fded346fafb04fc112c4b2b-7b079.png?1572600192" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="\vec{v}=(v_1,v_2)" width="100" /></span><br />
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Estas ecuaciones que os pongo aquí debajo son seis formas distintas de expresar la recta, en realidad son la misma recta pero expresada de distinta manera. Después iremos haciendo ejercicios para que entendáis lo que significan, así que tenerlas presentes, luego</span><span style="color: #274e13; font-family: "verdana" , sans-serif;"> con los ejercicios iremos familiarizándonos con ellas así que no os agobiéis, iremos poco a poco. </span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">La ecuaciones de la recta son la manera de expresarla pero no son ecuaciones que tengamos que resolver (recordar que las rectas tienen infinitos puntos y por eso tendrían infinitas soluciones) sino una manera de expresar los infinitos puntos de la recta.</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Vamos a ver ahora todas las fórmulas y después pasaremos a los ejercicios.</span></div>
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<tr class="row_first"><th id="id4867_c0" style="border-top: 0px; line-height: 22px; padding: 8px; text-align: left; vertical-align: bottom;">Ecuación</th><th id="id4867_c1" style="border-top: 0px; line-height: 22px; padding: 8px; text-align: left; vertical-align: bottom;">Fórmula</th><th id="id4867_c2" style="border-top: 0px; line-height: 22px; padding: 8px; text-align: left; vertical-align: bottom;">¿Cómo se obtiene?</th></tr>
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<tr class="row_odd odd"><td headers="id4867_c0" style="background-color: #f9f9f9; border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;">Vectorial</td><td headers="id4867_c1" style="background-color: #f9f9f9; border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;"><img alt="(x,y) = (x_0,y_0) + t \cdot (v_1,v_2)" height="42" src="https://matematicasies.com/local/cache-vignettes/L240xH42/ff5436ef61a80c2b58c4090e801e4e82-55e9d.png?1572632525" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="(x,y) = (x_0,y_0) + t \cdot (v_1,v_2)" width="240" /></td><td headers="id4867_c2" style="background-color: #f9f9f9; border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;">Punto y vector director</td></tr>
<tr class="row_even even"><td headers="id4867_c0" style="border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;">Paramétricas</td><td headers="id4867_c1" style="border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;"><img alt="\left \{ \begin{array}{ll}
x = x_0 + t \cdot v_1 \\
y = y_0 + t \cdot v_2
\end{array} \right. " height="72" src="https://matematicasies.com/local/cache-vignettes/L143xH72/7def960203768777922feb6c158cfd58-2b4af.png?1572632525" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="\left \{ \begin{array}{ll}
x = x_0 + t \cdot v_1 \\
y = y_0 + t \cdot v_2
\end{array} \right. " width="143" /></td><td headers="id4867_c2" style="border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;">Punto y vector director</td></tr>
<tr class="row_odd odd"><td headers="id4867_c0" style="background-color: #f9f9f9; border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;">Continua</td><td headers="id4867_c1" style="background-color: #f9f9f9; border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;"><img alt="\frac{x-x_0}{v_1} = \frac{y-y_0}{v_2} " height="63" src="https://matematicasies.com/local/cache-vignettes/L142xH63/c5e36b6f3d7514a80d6073a7820905fb-6024e.png?1572601106" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="\frac{x-x_0}{v_1} = \frac{y-y_0}{v_2} " width="142" /></td><td headers="id4867_c2" style="background-color: #f9f9f9; border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;">Punto y vector director</td></tr>
<tr class="row_even even"><td headers="id4867_c0" style="border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;">General</td><td headers="id4867_c1" style="border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;"><img alt="Ax + By + C = 0" height="40" src="https://matematicasies.com/local/cache-vignettes/L155xH40/f9154d650698f0862b4f99fa0bae0029-0eac6.png?1572626602" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="Ax + By + C = 0" width="155" /></td><td headers="id4867_c2" style="border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;">Productos cruzados a partir de la ec. continua</td></tr>
<tr class="row_odd odd"><td headers="id4867_c0" style="background-color: #f9f9f9; border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;">Explícita</td><td headers="id4867_c1" style="background-color: #f9f9f9; border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;"><img alt="y = mx + n" height="37" src="https://matematicasies.com/local/cache-vignettes/L107xH37/112d608d870114e7d8181ab6449003a2-acbb1.png?1572658273" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="y = mx + n" width="107" /></td><td headers="id4867_c2" style="background-color: #f9f9f9; border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;">Despejando "<img alt="y" height="30" src="https://matematicasies.com/local/cache-vignettes/L15xH30/415290769594460e2e485922904f345d-4fae4.png?1572600153" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="y" width="15" />" en la ec. general</td></tr>
<tr class="row_even even"><td headers="id4867_c0" style="border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;">Punto-pendiente</td><td headers="id4867_c1" style="border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;"><img alt="y-y_0= m(x-x_0)" height="42" src="https://matematicasies.com/local/cache-vignettes/L170xH42/42997d19e7fb4a24f1c8be639676f799-b97f1.png?1572666089" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="y-y_0= m(x-x_0)" width="170" /></td><td headers="id4867_c2" style="border-top: 1px solid rgb(221, 221, 221); line-height: 22px; padding: 8px; vertical-align: top;">Punto y pendiente <img alt="m=\frac{v_2}{v_1}" height="57" src="https://matematicasies.com/local/cache-vignettes/L65xH57/af3ab177d949aae5d80b71f3fecc14ef-01769.png?1572666089" style="border: 0px; height: auto; max-width: 100%; vertical-align: middle;" title="m=\frac{v_2}{v_1}" width="65" /><br />
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">El ejercicio más básico en el tema de rectas es saber expresar las ecuaciones de la recta en las seis formas anteriores.</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Vamos a ir muy despacio y hoy empezamos solamente con la primera ecuación, la ecuación vectorial:</span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;"><b>ECUACIÓN VECTORIAL: (x,y)=(x<span style="font-size: xx-small;">0</span>,y<span style="font-size: xx-small;">0)+ </span>t(v<span style="font-size: xx-small;">1,</span>v<span style="font-size: xx-small;">2</span>) siendo t un número real</b></span></div>
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<span style="color: #274e13; font-family: "verdana" , sans-serif;">Lo que os sugiero ahora es que veáis el siguiente vídeo, hagáis los tres ejercicios que aparecen en el en vuestro cuaderno y después hagáis los que os propongo y no dejéis nunca de sorprenderme:</span></div>
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<span style="font-family: "verdana" , sans-serif;"><b>EJERCICIO 1:</b></span></div>
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<span style="font-family: "verdana" , sans-serif;"><span style="background-color: white; color: #222222; font-size: 16px;">Una recta pasa por el punto </span><span class="escarlata" style="background-color: white; background-repeat: no-repeat; box-sizing: inherit; color: #222222; font-size: 16px; margin: 0px; padding: 0px;">A</span><span style="background-color: white; color: #222222; font-size: 16px;">(-1, 3) y tiene un vector director </span><img alt="\vec{v} = (2,5)" class="ql-img-inline-formula" src="https://www.superprof.es/apuntes/wp-content/ql-cache/quicklatex.com-4b57693d832011ec1e54fdb84163f243_l3.png" style="background-attachment: initial !important; background-clip: initial !important; background-color: white; background-image: none !important; background-origin: initial !important; background-position: initial !important; background-repeat: initial !important; background-size: initial !important; border: none !important; box-sizing: inherit; color: #222222; font-size: 16px; height: auto; margin: 0px !important; max-width: 100%; padding: 0px !important; vertical-align: -6px;" title="Rendered by QuickLaTeX.com" /><span style="background-color: white; color: #222222; font-size: 16px;">. Escribir su ecuación vectorial.</span></span></div>
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<b style="font-family: Verdana, sans-serif;">EJERCICIO 2:</b></div>
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<span style="font-family: "verdana" , sans-serif;">Hallar la ecuación vectorial de la recta que pasa por los puntos A(-2,1) y B(3,4).</span></div>
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<span style="font-family: "verdana" , sans-serif;"><b>EJERCICIO 3:</b></span></div>
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<span style="font-family: "verdana" , sans-serif;">Dada la recta cuya ecuación vectorial es (x,y)=(2,3)+t(1,2) indica cuatro puntos de dicha recta.</span></div>
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<span style="font-family: "verdana" , sans-serif;"><b>EJERCICIO 4:</b></span></div>
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<span style="font-family: "verdana" , sans-serif;">Representa en el plano la recta de ecuación </span><span style="font-family: "verdana" , sans-serif;">(x,y)=(2,3)+t(1,2).</span></div>
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<span style="font-family: "verdana" , sans-serif;"><b>EJERCICIO 5: </b></span></div>
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<span style="font-family: "verdana" , sans-serif;">Halla la ecuación vectorial de la recta que pasa por P(0,1) y tiene por vector director v(-1,2)</span></div>
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<span style="font-family: "verdana" , sans-serif;"><b>EJERCICIO 6:</b></span></div>
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<span style="font-family: "verdana" , sans-serif;">Dada la ecuación vectorial de la recta (x,y)=(-1,5)+t(3,-1) indica un punto y un vector de dicha recta.</span></div>
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<span style="font-family: "verdana" , sans-serif;">Como siempre cualquier duda la responderé en el mail: direccionpondal@gmail.com</span></div>
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<span style="font-family: "verdana" , sans-serif;"><b>SOLUCIONES:</b></span></h2>
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