{"id":27908,"date":"2024-08-15T19:51:16","date_gmt":"2024-08-15T19:51:16","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27908"},"modified":"2024-08-15T19:51:16","modified_gmt":"2024-08-15T19:51:16","slug":"problemes-resolus-limites-finies","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/fr\/problemes-resolus-limites-finies\/","title":{"rendered":"Probl\u00e8mes R\u00e9solus : Limites Finies"},"content":{"rendered":"<p><center><\/p>\n<h1>Probl\u00e8mes R\u00e9solus : Limites Finies<\/h1>\n<p><em><strong>R\u00e9sum\u00e9 :<\/strong><br \/>\nCe cours propose des probl\u00e8mes r\u00e9solus sur le calcul des limites finies, accompagn\u00e9s d&#8217;un tutoriel vid\u00e9o. Les \u00e9tudiants sont guid\u00e9s pour r\u00e9soudre les probl\u00e8mes et comparer leurs r\u00e9sultats avec les solutions fournies. L&#8217;accent est mis sur des techniques cl\u00e9s telles que la rationalisation et l&#8217;utilisation de graphiques, encourageant diff\u00e9rentes approches pour parvenir \u00e0 la bonne r\u00e9ponse.<\/em><\/p>\n<p><strong>Objectifs d&#8217;Apprentissage<\/strong><br \/>\n\u00c0 la fin de ce cours, l&#8217;\u00e9tudiant sera capable de :<\/p>\n<ul style=\"text-align:left;\">\n<li><strong>Calculer<\/strong> les limites finies des fonctions polynomiales et rationnelles.<\/li>\n<li><strong>Utiliser<\/strong> des techniques de rationalisation pour simplifier les calculs de limites.<\/li>\n<li><strong>Comparer<\/strong> diff\u00e9rentes m\u00e9thodes de r\u00e9solution et reconna\u00eetre qu&#8217;il existe plusieurs chemins pour arriver \u00e0 la solution correcte.<\/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;\">Ces exercices r\u00e9solus vous aideront \u00e0 ma\u00eetriser le calcul des limites finies. Les solutions sont dans la vid\u00e9o.<\/p>\n<p style=\"text-align: justify; color: #000000;\">Pour am\u00e9liorer l&#8217;exp\u00e9rience d&#8217;apprentissage, j&#8217;ai cr\u00e9\u00e9 cette vid\u00e9o avec des exercices r\u00e9solus sur le calcul des limites, montrant toutes les particularit\u00e9s qui peuvent en \u00eatre d\u00e9duites.<\/p>\n<p style=\"text-align: justify; color: #000000;\">Essayez de r\u00e9soudre ces exercices par vous-m\u00eame, puis comparez vos r\u00e9sultats.<br \/>\n\u00c0 c\u00f4t\u00e9 de chaque exercice, vous trouverez un lien qui m\u00e8ne \u00e0 la partie de la vid\u00e9o YouTube o\u00f9 tous les calculs sont effectu\u00e9s jusqu&#8217;\u00e0 la solution.<\/p>\n<p style=\"text-align: justify; color: #000000;\">Parfois, vous devrez rationaliser, et d&#8217;autres fois, vous devrez vous appuyer sur la d\u00e9finition de la limite pour justifier une r\u00e9ponse. Parfois, m\u00eame un graphique peut vous faire gagner beaucoup de temps pour d\u00e9cider quelle ligne de raisonnement suivre.<\/p>\n<h3>I. Calculez les limites finies suivantes :<\/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;\">[SOLUTION]<\/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;\">[SOLUTION]<\/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;\">[SOLUTION]<\/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;\">[SOLUTION]<\/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;\">[SOLUTION]<\/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;\">[SOLUTION]<\/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;\">[SOLUTION]<\/span><\/strong><\/a><\/li>\n<\/ol>\n<h3>II. Trouvez <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> pour les fonctions suivantes :<\/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;\">[SOLUTION]<\/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;\">[SOLUTION]<\/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;\">[SOLUTION]<\/span><\/strong><\/a><\/li>\n<\/ol>\n<p style=\"text-align: justify; color: #000000;\">Avez-vous r\u00e9ussi \u00e0 tous les r\u00e9soudre par vous-m\u00eame ?<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u00c0 quel point vos solutions sont-elles diff\u00e9rentes des miennes ?<\/p>\n<p style=\"text-align: justify; color: #000000;\">N&#8217;oubliez pas que le chemin pour r\u00e9soudre un probl\u00e8me n&#8217;est pas n\u00e9cessairement unique.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Probl\u00e8mes R\u00e9solus : Limites Finies R\u00e9sum\u00e9 : Ce cours propose des probl\u00e8mes r\u00e9solus sur le calcul des limites finies, accompagn\u00e9s d&#8217;un tutoriel vid\u00e9o. Les \u00e9tudiants sont guid\u00e9s pour r\u00e9soudre les probl\u00e8mes et comparer leurs r\u00e9sultats avec les solutions fournies. L&#8217;accent est mis sur des techniques cl\u00e9s telles que la rationalisation et l&#8217;utilisation de graphiques, encourageant [&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":[866,569],"tags":[],"class_list":["post-27908","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-calcul-differentiel","category-mathematiques"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Probl\u00e8mes R\u00e9solus : Limites Finies - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Ma\u00eetrisez le calcul des limites finies avec ce cours qui inclut des probl\u00e8mes r\u00e9solus. 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