{"id":27883,"date":"2024-08-15T19:51:16","date_gmt":"2024-08-15T19:51:16","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27883"},"modified":"2024-08-15T19:51:16","modified_gmt":"2024-08-15T19:51:16","slug":"problemas-resueltos-limites-finitos","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/es\/problemas-resueltos-limites-finitos\/","title":{"rendered":"Problemas Resueltos: L\u00edmites Finitos"},"content":{"rendered":"<p><center><\/p>\n<h1>Problemas Resueltos: L\u00edmites Finitos<\/h1>\n<p><em><strong>Resumen:<\/strong><br \/>\nEsta clase ofrece problemas resueltos sobre el c\u00e1lculo de l\u00edmites finitos, acompa\u00f1ados de un video tutorial. Los estudiantes son guiados para resolver los problemas y comparar sus resultados con las soluciones proporcionadas. Se destacan t\u00e9cnicas clave como la racionalizaci\u00f3n y el uso de gr\u00e1ficos, fomentando diferentes enfoques para alcanzar la respuesta correcta.<\/em><\/p>\n<p><strong>Objetivos de Aprendizaje<\/strong><br \/>\nAl finalizar esta clase el estudiante ser\u00e1 capaz de:<\/p>\n<ul style=\"text-align:left;\">\n<li><strong>Calcular<\/strong> l\u00edmites finitos de funciones polin\u00f3micas y racionales.<\/li>\n<li><strong>Utilizar<\/strong> t\u00e9cnicas de racionalizaci\u00f3n para simplificar c\u00e1lculos de l\u00edmites.<\/li>\n<li><strong>Comparar<\/strong> diferentes m\u00e9todos de resoluci\u00f3n y reconocer la existencia de m\u00faltiples caminos hacia la soluci\u00f3n correcta.<\/li>\n<\/ul>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/VY1gr1EUq3o\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">Estos ejercicios resueltos te servir\u00e1n de ayuda para lograr dominar el c\u00e1lculo de l\u00edmites finitos. Las soluciones est\u00e1n en el video.<\/p>\n<p style=\"text-align: justify; color: #000000;\">Para mejorar la experiencia de aprendizaje, he creado este v\u00eddeo con ejercicios resueltos de c\u00e1lculo de l\u00edmites, mostrando todas las particularidades que de ellos se pueden inferir.<\/p>\n<p style=\"text-align: justify; color: #000000;\">Intenta resolver estos ejercicios por tu cuenta y luego compara tus resultados.<br \/>\nJunto a cada ejercicio encontrar\u00e1s un enlace que conduce a la parte del v\u00eddeo de youtube en donde se realizan todos los c\u00e1lculos hasta llegar a su soluci\u00f3n.<\/p>\n<p style=\"text-align: justify; color: #000000;\">En ocasiones tendr\u00e1s que racionalizar y en otras tendr\u00e1s que apoyarte en la definici\u00f3n de l\u00edmite para justificar una respueta. A veces incluso un gr\u00e1fico te puede ahorrar mucho trabajo a la hora de decidir qu\u00e9 linea de razonamiento seguir.<\/p>\n<h3>I. Calcule los siguientes l\u00edmites finitos:<\/h3>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -1} (x^3+2x^2 - 3x - 4) <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=35s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[SOLUCI\u00d3N]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 0} \\dfrac{3^x - 3^{-x}}{3^x + 3^{-x}} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=64s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[SOLUCI\u00d3N]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2} \\dfrac{x-1}{x^2-1} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=91s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[SOLUCI\u00d3N]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2} \\dfrac{x^2-4}{x^2-5x+6} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=161s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[SOLUCI\u00d3N]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -1} \\dfrac{x^2+3x+2}{x^2+4x+3} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=351s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[SOLUCI\u00d3N]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2} \\dfrac{x-2}{\\sqrt{x^2-4}} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=594s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[SOLUCI\u00d3N]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2} \\dfrac{\\sqrt{x-2}}{x^2-4} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=887s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[SOLUCI\u00d3N]<\/span><\/strong><\/a><\/li>\n<\/ol>\n<h3>II. Hallar <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{h\\to 0} \\frac{f(x+h)-f(x)}{h}<\/span><\/span> para las siguientes funciones:<\/h3>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f(x) = \\dfrac{1}{x-2} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=1088s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[SOLUCI\u00d3N]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f(x) = \\sqrt{x-4} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=1263s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[SOLUCI\u00d3N]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f(x) = \\dfrac{x}{x+1} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=1366s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[SOLUCI\u00d3N]<\/span><\/strong><\/a><\/li>\n<\/ol>\n<p style=\"text-align: justify; color: #000000;\">\u00bfHas logrado resolverlos todos por tu propia cuenta?.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u00bfQu\u00e9 tan distintos son tus desarrollos de los m\u00edos?.<\/p>\n<p style=\"text-align: justify; color: #000000;\">Recuerda que el camino para resolver un problema no es \u00fanico por necesidad.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problemas Resueltos: L\u00edmites Finitos Resumen: Esta clase ofrece problemas resueltos sobre el c\u00e1lculo de l\u00edmites finitos, acompa\u00f1ados de un video tutorial. Los estudiantes son guiados para resolver los problemas y comparar sus resultados con las soluciones proporcionadas. Se destacan t\u00e9cnicas clave como la racionalizaci\u00f3n y el uso de gr\u00e1ficos, fomentando diferentes enfoques para alcanzar la [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27893,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":331,"footnotes":""},"categories":[852,563],"tags":[],"class_list":["post-27883","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-calculo-diferencial","category-matematica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Problemas Resueltos: L\u00edmites Finitos - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Domina el c\u00e1lculo de l\u00edmites finitos con esta clase que incluye problemas resueltos. 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