{"id":27897,"date":"2024-08-15T19:51:15","date_gmt":"2024-08-15T19:51:15","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27897"},"modified":"2024-08-15T19:51:15","modified_gmt":"2024-08-15T19:51:15","slug":"problemas-resolvidos-limites-finitos","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/pt\/problemas-resolvidos-limites-finitos\/","title":{"rendered":"Problemas Resolvidos: Limites Finitos"},"content":{"rendered":"<p><center><\/p>\n<h1>Problemas Resolvidos: Limites Finitos<\/h1>\n<p><em><strong>Resumo:<\/strong><br \/>\nEsta aula oferece problemas resolvidos sobre o c\u00e1lculo de limites finitos, acompanhados de um v\u00eddeo tutorial. Os alunos s\u00e3o guiados para resolver os problemas e comparar seus resultados com as solu\u00e7\u00f5es fornecidas. T\u00e9cnicas chave como a racionaliza\u00e7\u00e3o e o uso de gr\u00e1ficos s\u00e3o destacadas, incentivando diferentes abordagens para chegar \u00e0 resposta correta.<\/em><\/p>\n<p><strong>Objetivos de Aprendizagem<\/strong><br \/>\nAo final desta aula, o aluno ser\u00e1 capaz de:<\/p>\n<ul style=\"text-align:left;\">\n<li><strong>Calcular<\/strong> limites finitos de fun\u00e7\u00f5es polinomiais e racionais.<\/li>\n<li><strong>Utilizar<\/strong> t\u00e9cnicas de racionaliza\u00e7\u00e3o para simplificar c\u00e1lculos de limites.<\/li>\n<li><strong>Comparar<\/strong> diferentes m\u00e9todos de resolu\u00e7\u00e3o e reconhecer a exist\u00eancia de m\u00faltiplos caminhos para a solu\u00e7\u00e3o correta.<\/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;\">Esses exerc\u00edcios resolvidos ajudar\u00e3o voc\u00ea a dominar o c\u00e1lculo de limites finitos. As solu\u00e7\u00f5es est\u00e3o no v\u00eddeo.<\/p>\n<p style=\"text-align: justify; color: #000000;\">Para melhorar a experi\u00eancia de aprendizado, criei este v\u00eddeo com exerc\u00edcios resolvidos sobre o c\u00e1lculo de limites, mostrando todas as particularidades que podem ser inferidas deles.<\/p>\n<p style=\"text-align: justify; color: #000000;\">Tente resolver esses exerc\u00edcios por conta pr\u00f3pria e depois compare seus resultados.<br \/>\nAo lado de cada exerc\u00edcio, voc\u00ea encontrar\u00e1 um link que leva \u00e0 parte do v\u00eddeo no YouTube onde todos os c\u00e1lculos s\u00e3o realizados at\u00e9 a solu\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u00c0s vezes, voc\u00ea ter\u00e1 que racionalizar e, em outras, ter\u00e1 que se basear na defini\u00e7\u00e3o de limite para justificar uma resposta. \u00c0s vezes, at\u00e9 mesmo um gr\u00e1fico pode economizar muito trabalho na hora de decidir qual linha de racioc\u00ednio seguir.<\/p>\n<h3>I. Calcule os seguintes limites 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;\">[SOLU\u00c7\u00c3O]<\/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;\">[SOLU\u00c7\u00c3O]<\/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;\">[SOLU\u00c7\u00c3O]<\/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;\">[SOLU\u00c7\u00c3O]<\/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;\">[SOLU\u00c7\u00c3O]<\/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;\">[SOLU\u00c7\u00c3O]<\/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;\">[SOLU\u00c7\u00c3O]<\/span><\/strong><\/a><\/li>\n<\/ol>\n<h3>II. Encontre <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 as seguintes fun\u00e7\u00f5es:<\/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;\">[SOLU\u00c7\u00c3O]<\/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;\">[SOLU\u00c7\u00c3O]<\/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;\">[SOLU\u00c7\u00c3O]<\/span><\/strong><\/a><\/li>\n<\/ol>\n<p style=\"text-align: justify; color: #000000;\">Voc\u00ea conseguiu resolver todos por conta pr\u00f3pria?<\/p>\n<p style=\"text-align: justify; color: #000000;\">Qu\u00e3o diferentes s\u00e3o suas solu\u00e7\u00f5es das minhas?<\/p>\n<p style=\"text-align: justify; color: #000000;\">Lembre-se de que o caminho para resolver um problema n\u00e3o \u00e9 necessariamente \u00fanico.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problemas Resolvidos: Limites Finitos Resumo: Esta aula oferece problemas resolvidos sobre o c\u00e1lculo de limites finitos, acompanhados de um v\u00eddeo tutorial. Os alunos s\u00e3o guiados para resolver os problemas e comparar seus resultados com as solu\u00e7\u00f5es fornecidas. T\u00e9cnicas chave como a racionaliza\u00e7\u00e3o e o uso de gr\u00e1ficos s\u00e3o destacadas, incentivando diferentes abordagens para chegar \u00e0 [&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":2,"footnotes":""},"categories":[856,571],"tags":[],"class_list":["post-27897","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-calculo-diferencial-pt","category-matematica-pt"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Problemas Resolvidos: Limites Finitos - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Domine o c\u00e1lculo de limites finitos com esta aula que inclui problemas resolvidos. 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