{"id":133871,"date":"2023-03-11T16:45:54","date_gmt":"2023-03-11T11:15:54","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=133871"},"modified":"2023-03-11T16:45:54","modified_gmt":"2023-03-11T11:15:54","slug":"the-function-fx-x-where-a-denotes-the-greatest-integer-less-than-or-equal-to-x-is-continuous-at","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/the-function-fx-x-where-a-denotes-the-greatest-integer-less-than-or-equal-to-x-is-continuous-at","title":{"rendered":"The function f(x) = [x], where [a] denotes the greatest integer less than or equal to x, is continuous at"},"content":{"rendered":"<h2>These are the options for the Question: The function f(x) = [x], where [a] denotes the greatest integer less than or equal to x, is continuous at<\/h2>\n<h3>(a) x=1<br \/>\n(b) x = 1.5<br \/>\n(c) x=-2<br \/>\n(d) x=4<\/h3>\n<p>&nbsp;<\/p>\n<h4>The correct answer is &#8211;<\/h4>\n<div class=\"flex-1 overflow-hidden\">\n<div class=\"react-scroll-to-bottom--css-rydqy-79elbk h-full dark:bg-gray-800\">\n<div class=\"react-scroll-to-bottom--css-rydqy-1n7m0yu\">\n<div class=\"flex flex-col items-center text-sm dark:bg-gray-800\">\n<div class=\"group w-full text-gray-800 dark:text-gray-100 border-b border-black\/10 dark:border-gray-900\/50 bg-gray-50 dark:bg-[#444654]\">\n<div class=\"text-base gap-4 md:gap-6 md:max-w-2xl lg:max-w-2xl xl:max-w-3xl p-4 md:py-6 flex lg:px-0 m-auto\">\n<div class=\"relative flex w-[calc(100%-50px)] flex-col gap-1 md:gap-3 lg:w-[calc(100%-115px)]\">\n<div class=\"flex flex-grow flex-col gap-3\">\n<div class=\"min-h-[20px] flex flex-col items-start gap-4 whitespace-pre-wrap\">\n<div class=\"markdown prose w-full break-words dark:prose-invert light\">\n<p>The function f(x) = [x] is continuous for all values of x except for integers, where it has jump discontinuities. At integer values, the function changes value suddenly by 1.<\/p>\n<p>Therefore, the function f(x) = [x] is continuous at all values of x except for integers.<\/p>\n<p>Answer: None of the options (a), (b), (c), or (d) are correct.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"flex justify-between\">\n<div class=\"text-gray-400 flex self-end lg:self-center justify-center mt-2 gap-3 md:gap-4 lg:gap-1 lg:absolute lg:top-0 lg:translate-x-full lg:right-0 lg:mt-0 lg:pl-2 visible\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"w-full h-32 md:h-48 flex-shrink-0\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"absolute bottom-0 left-0 w-full border-t md:border-t-0 dark:border-white\/20 md:border-transparent md:dark:border-transparent md:bg-vert-light-gradient bg-white dark:bg-gray-800 md:!bg-transparent dark:md:bg-vert-dark-gradient\">\n<form class=\"stretch mx-2 flex flex-row gap-3 last:mb-2 md:last:mb-6 lg:mx-auto lg:max-w-3xl\">\n<div class=\"relative flex h-full flex-1 md:flex-col\">\n<div class=\"flex ml-1 mt-1.5 md:w-full md:m-auto md:mb-2 gap-0 md:gap-2 justify-center\"><\/div>\n<\/div>\n<\/form>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>These are the options for the Question: The function f(x) = [x], where [a] denotes the greatest integer less than or equal to x, is continuous at (a) x=1 (b) x = 1.5 (c) x=-2 (d) x=4 &nbsp; The correct answer is &#8211; The function f(x) = [x] is continuous for all values of x [&hellip;]<\/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-133871","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\/133871","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=133871"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133871\/revisions"}],"predecessor-version":[{"id":133874,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133871\/revisions\/133874"}],"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=133871"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=133871"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=133871"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}