{"id":5883,"date":"2025-08-08T11:19:34","date_gmt":"2025-08-08T05:49:34","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=5883"},"modified":"2025-08-08T11:20:47","modified_gmt":"2025-08-08T05:50:47","slug":"continuity","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ee\/calculus-and-differeential-equations\/continuity","title":{"rendered":"Continuity"},"content":{"rendered":"<h2><strong>Definition of Continuity<\/strong><\/h2>\n<p>A function f(x) is defined for x = a is said to be continuous at x = a if:<\/p>\n<p><strong>1.<\/strong> f(a), i.e., the value of f(x) at x = a is a definite number and<\/p>\n<p><strong>2.<\/strong> The limit of the function f(x) as x \u2192 a exists and is equal to the value of f(x) at x = a.<\/p>\n<p>Note: On comparing the definitions of limit and continuity we find that a function f(x) is continuous at x=a if<\/p>\n<p>Limit f(x)=f(a)<br \/>\nx\u2192a<\/p>\n<p>Thus f(x) is continuous at x = a if we have f(a + 0) = f(a \u2013 0) = f(a), otherwise it is discontinuous at\u00a0x = a.<\/p>\n<h3>Continuity in an Open Interval<\/h3>\n<p>A function f is said to be continuous in the open interval (a, b), if it is continuous at each point of open interval.<\/p>\n<h3>Continuity in a Closed Interval<\/h3>\n<p>Let f be a function defined on the closed interval (a, b) f is said to be continuous on the closed interval [a, b] if it is:<\/p>\n<p><strong> 1.<\/strong> continuous from the right at a and<\/p>\n<p><strong> 2.<\/strong> continuous from the left at b and<\/p>\n<p><strong> 3.<\/strong> continuous on the open interval (a, b).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Definition of Continuity A function f(x) is defined for x = a is said to be continuous at x =<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1733,5],"tags":[1737,1736],"class_list":["post-5883","post","type-post","status-publish","format-standard","hentry","category-calculus-and-differeential-equations","category-ee","tag-continuity-in-a-closed-interval","tag-continuity-in-an-open-interval"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5883","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=5883"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/5883\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=5883"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=5883"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=5883"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}