{"id":5071,"date":"2015-11-20T13:15:58","date_gmt":"2015-11-20T12:15:58","guid":{"rendered":"http:\/\/www.matematicaok.it\/?p=5071"},"modified":"2015-11-20T13:16:45","modified_gmt":"2015-11-20T12:16:45","slug":"teorema-di-de-lhopital","status":"publish","type":"post","link":"https:\/\/www.matematicaok.com\/?p=5071","title":{"rendered":"Teorema di De L&#8217;H\u00f4pital"},"content":{"rendered":"<p>Siano date due funzioni f(x) e g(x), che supponiamo definite e derivabili in tutti i punti di un intorno I del punto c (finito o\u00a0infinito), escluso al pi\u00f9 c stesso. Supponiamo inoltre che\u00a0che il limite del rapporto delle due funzioni,<a href=\"http:\/\/www.matematicaok.it\/wp-content\/uploads\/2015\/11\/Hopital1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5072 \" src=\"http:\/\/www.matematicaok.it\/wp-content\/uploads\/2015\/11\/Hopital1-300x215.png\" alt=\"Hopital1\" width=\"120\" height=\"86\" srcset=\"https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/Hopital1-300x215.png 300w, https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/Hopital1.png 447w\" sizes=\"auto, (max-width: 120px) 100vw, 120px\" \/><\/a>si presenti in una forma indeterminata del tipo [0 su 0]\u00a0oppure \u00a0[infinito su infinito] e sia g'(x)\u22600\u00a0in tutti i punti di I, escluso al pi\u00f9 x = c.\u00a0In tali ipotesi, se esiste il limite del rapporto delle derivate<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.matematicaok.it\/wp-content\/uploads\/2015\/11\/Hopital2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5073\" src=\"http:\/\/www.matematicaok.it\/wp-content\/uploads\/2015\/11\/Hopital2-300x180.png\" alt=\"Hopital2\" width=\"126\" height=\"75\" srcset=\"https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/Hopital2-300x180.png 300w, https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/Hopital2.png 496w\" sizes=\"auto, (max-width: 126px) 100vw, 126px\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><strong>allora<\/strong><\/p>\n<p style=\"text-align: left;\"><a href=\"http:\/\/www.matematicaok.it\/wp-content\/uploads\/2015\/11\/Hopital3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-5074\" src=\"http:\/\/www.matematicaok.it\/wp-content\/uploads\/2015\/11\/Hopital3-300x106.png\" alt=\"Hopital3\" width=\"300\" height=\"106\" srcset=\"https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/Hopital3-300x106.png 300w, https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/Hopital3.png 892w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p style=\"text-align: left;\">\n","protected":false},"excerpt":{"rendered":"<p>Siano date due funzioni f(x) e g(x), che supponiamo definite e derivabili in tutti i punti di un intorno I del punto c (finito o\u00a0infinito), escluso al pi\u00f9 c stesso. Supponiamo inoltre che\u00a0che il limite del rapporto delle due funzioni,si presenti in una forma indeterminata del tipo [0 su 0]\u00a0oppure \u00a0[infinito su infinito] e sia g'(x)\u22600\u00a0in tutti i punti di I, escluso al pi\u00f9 x = c.\u00a0In tali ipotesi, se&hellip; <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[207],"tags":[],"class_list":["post-5071","post","type-post","status-publish","format-standard","hentry","category-teorema-de-lhopital"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p85Wmq-1jN","_links":{"self":[{"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/posts\/5071","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5071"}],"version-history":[{"count":2,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/posts\/5071\/revisions"}],"predecessor-version":[{"id":5076,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/posts\/5071\/revisions\/5076"}],"wp:attachment":[{"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5071"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5071"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5071"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}