{"id":133940,"date":"2023-03-12T16:41:41","date_gmt":"2023-03-12T11:11:41","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=133940"},"modified":"2023-03-12T16:42:05","modified_gmt":"2023-03-12T11:12:05","slug":"a-find-the-value-of-k-for-which-the-function-f-given-as-fx1-cos-x-2x2-if-x0-is-continuous-at-x0-k-ifx0","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/a-find-the-value-of-k-for-which-the-function-f-given-as-fx1-cos-x-2x2-if-x0-is-continuous-at-x0-k-ifx0","title":{"rendered":"Find the value of K for which the function F given as f(x)={1-cos x\/2×2, if x=0 is continuous at x=0 K ifx=0"},"content":{"rendered":"

Question: Find the value of K for which the function F given as f(x)={1-cos x\/2×2, if x=0 is continuous at x=0 K ifx=0<\/h2>\n

 <\/p>\n

The correct answer is –<\/h3>\n

To find the value of K for which the function f(x) is continuous at x=0, we need to evaluate the limit of f(x) as x approaches 0 and compare it with the value of f(0).<\/h4>\n

First, let’s substitute x=0 into the given function:<\/h4>\n

f(0) = (1 – cos(0)) \/ (2*0^2) = 0\/0, which is an indeterminate form.<\/h4>\n

To evaluate the limit of f(x) as x approaches 0, we can use L’Hopital’s rule:<\/h4>\n

lim x\u21920 [1 – cos(x)] \/ (2x^2) = lim x\u21920 [sin(x)] \/ (4x) = lim x\u21920 [cos(x)] \/ 4 = 1\/4<\/h4>\n

Therefore, to make f(x) continuous at x=0, we need to choose K such that:<\/h4>\n

K = 1\/4<\/h4>\n

So, the value of K for which the function f(x) is continuous at x=0 is 1\/4.<\/h4>\n","protected":false},"excerpt":{"rendered":"

Question: Find the value of K for which the function F given as f(x)={1-cos x\/2×2, if x=0 is continuous at x=0 K ifx=0   The correct answer is – To find the value of K for which the function f(x) is continuous at x=0, we need to evaluate the limit of f(x) as x approaches […]<\/p>\n","protected":false},"author":21842,"featured_media":132233,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12119],"tags":[],"class_list":{"0":"post-133940","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-quiz"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133940","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21842"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=133940"}],"version-history":[{"count":2,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133940\/revisions"}],"predecessor-version":[{"id":133942,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133940\/revisions\/133942"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/132233"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=133940"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=133940"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=133940"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}