{"id":19588,"date":"2017-01-13T21:15:03","date_gmt":"2017-01-13T21:15:03","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=19588"},"modified":"2017-01-13T21:17:41","modified_gmt":"2017-01-13T21:17:41","slug":"calculus-lhopitals-rule-limx%e2%86%92%e2%88%9e-lnxsquare-root-x","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/calculus-lhopitals-rule-limx%e2%86%92%e2%88%9e-lnxsquare-root-x\/","title":{"rendered":"Calculus:  l&#8217;H\u00f4pital&#8217;s rule:  lim(x\u2192\u221e) lnx\/square root x"},"content":{"rendered":"<h1>The tutor uses l&#8217;H\u00f4pital&#8217;s rule to find a limit of form \u221e\/\u221e.<\/h1>\n<p>l&#8217;H\u00f4pital&#8217;s rule states that the limit of a quotient of form \u221e\/\u221e or 0\/0 can be found as follows:<\/p>\n<p>lim (f(x)\/g(x)) = lim (f'(x)\/g'(x))<\/p>\n<p>In this case [noting the square root of x is x<sup>0.5<\/sup>]:<\/p>\n<p>lim<sub>x\u2192\u221e<\/sub>(lnx\/x<sup>0.5<\/sup>) = (by l&#8217;H\u00f4pital) lim<sub>x\u2192\u221e<\/sub>((x<sup>-1<\/sup>)\/(0.5x<sup>-0.5<\/sup>))<\/p>\n<p>which becomes <\/p>\n<p>lim<sub>x\u2192\u221e<\/sub>2x<sup>-0.5<\/sup> or lim<sub>x\u2192\u221e<\/sub>2\/x<sup>0.5<\/sup> = 0<\/p>\n<p>By that reasoning, the reciprocal limit, lim<sub>x\u2192\u221e<\/sub>(x<sup>0.5<\/sup>\/lnx), should not exist.<\/p>\n<p>Source:<\/p>\n<p>Larson, Roland E. and Robert P. Hostetler.  <u>Calculus,<\/u> 3rd ed.  Toronto:  DC Heath, 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 uses l&#8217;H\u00f4pital&#8217;s rule to find a limit of form \u221e\/\u221e. l&#8217;H\u00f4pital&#8217;s rule states that the limit of a quotient of form \u221e\/\u221e or 0\/0 can be found as follows: lim (f(x)\/g(x)) = lim (f'(x)\/g'(x)) In this case [noting &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/calculus-lhopitals-rule-limx%e2%86%92%e2%88%9e-lnxsquare-root-x\/\"> <span class=\"screen-reader-text\">Calculus:  l&#8217;H\u00f4pital&#8217;s rule:  lim(x\u2192\u221e) lnx\/square root x<\/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],"tags":[792,1894,2102],"class_list":["post-19588","post","type-post","status-publish","format-standard","hentry","category-calculus","tag-lhopitals-rule","tag-limits","tag-lnxx0-5"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/19588","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=19588"}],"version-history":[{"count":8,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/19588\/revisions"}],"predecessor-version":[{"id":19596,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/19588\/revisions\/19596"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=19588"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=19588"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=19588"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}