{"id":2626,"date":"2006-09-05T00:00:00","date_gmt":"2006-09-04T22:00:00","guid":{"rendered":""},"modified":"-0001-11-30T00:00:00","modified_gmt":"-0001-11-29T22:00:00","slug":"2626","status":"publish","type":"post","link":"https:\/\/www.vialattea.net\/content\/2626\/","title":{"rendered":"salve, vorrei esposto il teorema di una funzione derivabile e continua.grazie mille"},"content":{"rendered":"<div style=\"text-align: left;\">Immagino che la domanda posta faccia riferimento al Teorema che afferma che se f \u00e8 derivabile, allora \u00e8 continua.<\/p>\n<p><span style=\"font-weight: bold;\">TEOREMA: <\/span><span style=\"font-style: italic;\">Sia f:(a,b)-&gt;<span style=\"font-weight: bold;\">R<\/span> una funzione derivabile; allora f \u00e8 continua.<\/p>\n<p><span style=\"font-style: italic;\">Dimostrazione. <\/span><\/span>Siano x<sub>0<\/sub> &#8712;(a,b) e h &#8712; <span style=\"font-weight: bold;\">R<\/span> abbastanza piccolo; allora si ha f(x<sub>0<\/sub>+h)=h [f(x<sub>0<\/sub>+h)-f(x<sub>0<\/sub>)] \/ h +f(x<sub>0<\/sub>). Per h-&gt;0, [f(x<sub>0<\/sub>+h)-f(x<sub>0<\/sub>)] \/ h -&gt; f'(x<sub>0<\/sub>) &#8712; <span style=\"font-weight: bold;\">R<\/span>, per cui f(x<sub>0<\/sub>+h) -&gt; f(x<sub>0<\/sub>) che d\u00e0 la continuit\u00e0 di f in x<sub>0<\/sub>.<span style=\"font-style: italic;\"><span style=\"font-style: italic;\"\/><br type=\"_moz\"\/><\/span><\/div>\n","protected":false},"excerpt":{"rendered":"<p>[&#8230;]<\/p>\n","protected":false},"author":228,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[66],"tags":[],"class_list":["post-2626","post","type-post","status-publish","format-standard","hentry","category-analisi-matematica"],"_links":{"self":[{"href":"https:\/\/www.vialattea.net\/content\/wp-json\/wp\/v2\/posts\/2626","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vialattea.net\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vialattea.net\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vialattea.net\/content\/wp-json\/wp\/v2\/users\/228"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vialattea.net\/content\/wp-json\/wp\/v2\/comments?post=2626"}],"version-history":[{"count":0,"href":"https:\/\/www.vialattea.net\/content\/wp-json\/wp\/v2\/posts\/2626\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vialattea.net\/content\/wp-json\/wp\/v2\/media?parent=2626"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vialattea.net\/content\/wp-json\/wp\/v2\/categories?post=2626"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vialattea.net\/content\/wp-json\/wp\/v2\/tags?post=2626"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}