{"id":68,"date":"2024-05-29T23:49:42","date_gmt":"2024-05-29T23:49:42","guid":{"rendered":"https:\/\/formulariosemiserio.it\/?p=68"},"modified":"2024-05-29T23:49:44","modified_gmt":"2024-05-29T23:49:44","slug":"teoremi-di-lhospital-di-rolle-e-di-lagrange","status":"publish","type":"post","link":"https:\/\/formulariosemiserio.it\/?p=68","title":{"rendered":"Teoremi di L&#8217;Hospital, di Rolle e di Lagrange"},"content":{"rendered":"\n<!DOCTYPE html>\n<html lang=\"it\">\n<head>\n    <meta charset=\"UTF-8\">\n    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n   \n    <link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.12.0\/dist\/katex.min.css\">\n    <script defer src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.12.0\/dist\/katex.min.js\"><\/script>\n    <script defer src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.12.0\/dist\/contrib\/auto-render.min.js\"\n        onload=\"renderMathInElement(document.body);\"><\/script>\n    <style>\n       \n        section {\n            margin-bottom: 20px;\n        }\n    <\/style>\n<\/head>\n<body>\n\n\n<section>\n    <h4>Teorema di L&#8217;Hospital<\/h4>\n    <p>Il teorema di L&#8217;Hospital aiuta a calcolare i limiti delle forme indeterminate \\( \\frac{0}{0} \\) e \\( \\frac{\\infty}{\\infty} \\). Se \\( f(x) \\) e \\( g(x) \\) sono due funzioni derivabili in un intervallo e \\( \\lim_{{x \\to c}} f(x) = \\lim_{{x \\to c}} g(x) = 0 \\) o \\( \\pm\\infty \\), allora:<\/p>\n    <p>\\[\n        \\lim_{{x \\to c}} \\frac{f(x)}{g(x)} = \\lim_{{x \\to c}} \\frac{f'(x)}{g'(x)}\n    \\]<\/p>\n    <p>a condizione che il limite a destra esista.<\/p>\n<\/section>\n\n<section>\n    <h4>Teorema di Rolle<\/h4>\n    <p>Il teorema di Rolle afferma che se una funzione \\( f(x) \\) soddisfa le seguenti condizioni:<\/p>\n    <ul>\n        <li>\\( f(x) \\) \u00e8 continua in \\([a, b]\\),<\/li>\n        <li>\\( f(x) \\) \u00e8 derivabile in \\((a, b)\\),<\/li>\n        <li>\\( f(a) = f(b) \\),<\/li>\n    <\/ul>\n    <p>allora esiste almeno un punto \\( c \\) in \\((a, b)\\) tale che:<\/p>\n    <p>\\[\n        f'(c) = 0\n    \\]<\/p>\n<\/section>\n\n<section>\n    <h4>Teorema di Lagrange<\/h4>\n    <p>Il teorema di Lagrange, o teorema del valor medio, afferma che se una funzione \\( f(x) \\) \u00e8 continua in \\([a, b]\\) e derivabile in \\((a, b)\\), allora esiste almeno un punto \\( c \\) in \\((a, b)\\) tale che:<\/p>\n    <p>\\[\n        f'(c) = \\frac{f(b) &#8211; f(a)}{b &#8211; a}\n    \\]<\/p>\n<\/section>\n\n<\/body>\n<\/html>\n\n","protected":false},"excerpt":{"rendered":"<p>spiegazione dei Teoremi di L&#8217;Hospital, di Rolle e di Lagrange<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-68","post","type-post","status-publish","format-standard","hentry","category-le-derivate"],"_links":{"self":[{"href":"https:\/\/formulariosemiserio.it\/index.php?rest_route=\/wp\/v2\/posts\/68","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/formulariosemiserio.it\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/formulariosemiserio.it\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/formulariosemiserio.it\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/formulariosemiserio.it\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=68"}],"version-history":[{"count":1,"href":"https:\/\/formulariosemiserio.it\/index.php?rest_route=\/wp\/v2\/posts\/68\/revisions"}],"predecessor-version":[{"id":69,"href":"https:\/\/formulariosemiserio.it\/index.php?rest_route=\/wp\/v2\/posts\/68\/revisions\/69"}],"wp:attachment":[{"href":"https:\/\/formulariosemiserio.it\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=68"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/formulariosemiserio.it\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=68"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/formulariosemiserio.it\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=68"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}