{"id":17668,"date":"2016-09-04T06:30:16","date_gmt":"2016-09-04T06:30:16","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=17668"},"modified":"2016-09-04T06:30:16","modified_gmt":"2016-09-04T06:30:16","slug":"calculus-lhopitals-rule-another-proof-that-limx%e2%86%920-sinxx-1","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/calculus-lhopitals-rule-another-proof-that-limx%e2%86%920-sinxx-1\/","title":{"rendered":"Calculus:  l&#8217;H\u00f4pital&#8217;s rule:  another proof that lim<sub>x\u21920<\/sub> sinx\/x = 1"},"content":{"rendered":"<h1>The tutor shows that lim<sub>x\u21920<\/sub> sinx\/x = 1 using l&#8217;H\u00f4pital&#8217;s rule.<\/h1>\n<p>Put very simply, l&#8217;H\u00f4pital&#8217;s rule states that for a situation where Limit f(x)\/g(x) = 0\/0, Limit f(x)\/g(x) = Limit f'(x)\/g'(x), provided f(x), g(x) are both differentiable and so on.  Such is the exact premise of lim<sub>x\u21920<\/sub> sinx\/x.<\/p>\n<p>Using l&#8217;H\u00f4pital&#8217;s rule,<\/p>\n<p style=text-align:center\">lim<sub>x\u21920<\/sub> sinx\/x = lim<sub>x\u21920<\/sub> (sinx)&#8217;\/x&#8217; = lim<sub>x\u21920<\/sub> cosx\/1 = 1\/1 = 1<\/p>\n<p>Source:<\/p>\n<p>Larson, Roland and Robert Hostetler.  <u>Calculus<\/u>, 3rd ed.  Toronto:  D C Heath and Company, 1989.<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The tutor shows that limx\u21920 sinx\/x = 1 using l&#8217;H\u00f4pital&#8217;s rule. Put very simply, l&#8217;H\u00f4pital&#8217;s rule states that for a situation where Limit f(x)\/g(x) = 0\/0, Limit f(x)\/g(x) = Limit f'(x)\/g'(x), provided f(x), g(x) are both differentiable and so on. &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/calculus-lhopitals-rule-another-proof-that-limx%e2%86%920-sinxx-1\/\"> <span class=\"screen-reader-text\">Calculus:  l&#8217;H\u00f4pital&#8217;s rule:  another proof that lim<sub>x\u21920<\/sub> sinx\/x = 1<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[234,3],"tags":[1864,1863],"class_list":["post-17668","post","type-post","status-publish","format-standard","hentry","category-calculus","category-math","tag-proof-that-limit-x0-sinxx-1-using-lhopitals-rule","tag-proof-that-limx0-sinxx-1-using-lhopitals-rule"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17668","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=17668"}],"version-history":[{"count":7,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17668\/revisions"}],"predecessor-version":[{"id":17675,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17668\/revisions\/17675"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=17668"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=17668"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=17668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}