{"id":617904,"date":"2023-02-27T10:40:20","date_gmt":"2023-02-27T10:40:20","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=617904"},"modified":"2024-05-02T10:26:31","modified_gmt":"2024-05-02T10:26:31","slug":"ncert-exemplar-class-12-maths-chapter-5-continuity-and-differentiability","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/ncert-exemplar-class-12-maths-chapter-5-continuity-and-differentiability\/","title":{"rendered":"NCERT Exemplar Class 12 Maths Chapter 5: Continuity and Differentiability"},"content":{"rendered":"\n<p>NCERT Exemplar Class 12 Maths Chapter 5: Continuity and Differentiability. NCERT Exemplar Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability prepare students for their Class 12 exams thoroughly. <\/p>\n\n\n\n<p>Maths problems and solutions for the Class 12 pdf are provided here which are similar to the questions being asked in the previous year&#8217;s board. <\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-ncert-exemplar-class-12-maths-chapter-5-continuity-and-differentiability\"><strong>NCERT Exemplar Class 12 Maths Chapter 5: Continuity and Differentiability<\/strong><\/h2>\n\n\n\n<p>Class 12: Maths Chapter 5 solutions. Complete Class 12 Maths Chapter 5 Notes.<\/p>\n\n\n\n<p><strong>5.1 Overview<\/strong><br><strong>5.1.1 Continuity of a function at a point<\/strong><br>Let f be a real function on a subset of the real numbers and let c be a point in the domain of f. Then f is continuous at c if<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063353577_04a8ba6a89_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><br>More elaborately, if the left hand limit, right hand limit and the value of the function at x = c exist and are equal to each other, i.e.,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063353532_7c78cdb2d7_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>then f is said to be continuous at x = c.<\/p>\n\n\n\n<p><strong>5.1.2 Continuity in an interval<\/strong><\/p>\n\n\n\n<p>(i) f is said to be continuous in an open interval (a, b) if it is continuous at every point in this interval.<br>(ii) f is said to be continuous in the closed interval [a, b] if<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063358317_a834c09b8d_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>5.1.3 Geometrical meaning of continuity<\/strong><\/p>\n\n\n\n<p>(i) Function f will be continuous at x = c if there is no break in the graph of the function at the point (c,f(c)).<br>(ii) In an interval, function is said to be continuous if there is no break in the graph of the function in the entire interval.<\/p>\n\n\n\n<p><strong>5.1.4 Discontinuity<\/strong><\/p>\n\n\n\n<p>The function f will be discontinuous at x = a in any of the following cases :<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063150391_61385508ea_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>5.1.5 Continuity of some of the common functions<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062645373_70b0ff934e_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063379242_b55d650380_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>5.1.6 Continuity of composite functions<\/strong><\/p>\n\n\n\n<p>Let f and g be real valued functions such that (fog) is defined at a. If g is continuous at a and f is continuous at g (a), then (fog) is continuous at a.<\/p>\n\n\n\n<p><strong>5.1.7 Differentiability<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062656618_bc23976d6b_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>5.1.8 Algebra of derivatives<\/strong><\/p>\n\n\n\n<p>If u, v are functions of x, then<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063388252_5456d95da5_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>5.1.9<\/strong>&nbsp;Chain rule is a rule to differentiate composition of functions. Let f = vou. If<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062663483_917389789a_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>5.1.10<\/strong>&nbsp;Following are some of the standard derivatives (in appropriate domains)<\/p>\n\n\n\n<p>Click Here&nbsp;to download NCERT Exemplar Class 12 Maths Unit 5 Continuity and Differentiability.<\/p>\n\n\n\n<p><strong>5.1.11 Exponential and logarithmic functions<\/strong><\/p>\n\n\n\n<p>(i) The exponential function with positive base b &gt; 1 is the function y = f (x) = b<sup>x<\/sup>&nbsp;. Its domain is R, the set of all real numbers and range is the set of all positive real numbers. Exponential function with base 10 is called the common exponential function and with base e is called the natural exponential function.<br>(ii) Let b &gt; 1 be a real number. Then we say logarithm of a to base b is x if b<sup>x&nbsp;<\/sup>=a, Logarithm of a to the base b is denoted by log<sub>b<\/sub>&nbsp;a. If the base b = 10, we say it is common logarithm and if b = e, then we say it is natural logarithms. logx denotes the logarithm function to base e. The domain of logarithm function is R<sup>+<\/sup>&nbsp;, the set of all positive real numbers and the range is the set of all real numbers.<br>(iii) The properties of logarithmic function to any base b &gt; 1 are listed below:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063408997_f2c1dffa0c_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063408937_2b772bc844_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>5.1.12<\/strong>&nbsp;Logarithmic differentiation is a powerful technique to differentiate functions of the form f (x) = (u (x))&nbsp;<sup>v(x)<\/sup>&nbsp;, where both f and u need to be positive functions for this technique to make sense.<\/p>\n\n\n\n<p><strong>5.1.13<\/strong>&nbsp;Differentiation of a function with respect to another function<\/p>\n\n\n\n<p>Let u = f (x) and v = g (x) be two functions of x, then to find derivative of f (x) w.r.t. to g (x), i.e., to find<br>du\/dv , we use the formula<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063206016_41b2c56d3e_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>5.1.14 Second order derivative<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063422902_a757bcf52d_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>5.1.15 Rolle\u2019s Theorem<\/strong><\/p>\n\n\n\n<p>Let f : [a, b] \u2192 R be continuous on [a, b] and differentiable on (a, b), such that f (a) = f (b), where a and b are some real numbers. Then there exists at least one point c in (a, b) such that f \u2032 (c) = 0.<br>Geometrically Rolle\u2019s theorem ensures that there is at least one point on the curve y = f (x) at which tangent is parallel to x-axis (abscissa of the point lying in (a, b)).<\/p>\n\n\n\n<p><strong>5.1.16 Mean Value Theorem (Lagrange)<\/strong><\/p>\n\n\n\n<p>Let f : [a, b] \u2192 R be a continuous function on [a, b] and differentiable on (a, b). Then there exists at least one point c in (a, b) such that<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063431542_7074cfa5e6_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>Geometrically, Mean Value Theorem states that there exists at least one point c in (a, b) such that the tangent at the point (c, f (c)) is parallel to the secant joining the points (a, f (a) and (b, f (b)).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Short Answer Type Questions (Solved Examples)<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062728348_291cae2a64_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062728303_a8f36bae54_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063244451_4d19c3644c_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063456907_1203d21e50_o.png\"><\/h3>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063244396_f72aed6a3f_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063456827_704ff0c2d3_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062728128_25d8787043_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062728078_edb9cdc41a_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063456777_127748fce0_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062728013_2875ba8971_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063456752_f904a3c591_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063456722_66ab1d6e2f_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063456652_08137394e1_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063244036_9a2b507ca8_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Long Answer Type Questions (Solved Examples)<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063266881_bc73b115a6_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>Click Here&nbsp;to download NCERT Exemplar Class 12 Maths Unit 5 Continuity and Differentiability.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062751248_24a8dd7c47_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062751233_f1f7474dcd_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062751228_8fb940db57_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063266786_7c20cf7f8d_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063479602_7c2f93e53a_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062751148_2543899f8d_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063266691_feab4ea098_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062751073_a15e6c46b4_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Objective Type Questions (Solved Examples)<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063277656_d177eca34a_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063277601_ed070db9e6_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062762113_fc9ea95e49_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063490457_a45d734d74_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063277476_e4c328c632_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Match the Following (Solved Example)<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063295716_c10330d512_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063295691_a29064492a_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Fill in the Blanks (Solved Examples)<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062779773_9edbaa4666_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">True or False Statements Type Questions (Solved Examples)<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063295631_9810b4f543_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063295596_29b36f6a87_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Short Answer Type Questions (Exercise)<\/h3>\n\n\n\n<p>Click Here&nbsp;to download NCERT Exemplar Class 12 Maths Unit 5 Continuity and Differentiability.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Long Answer Type Questions (Exercise)<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/15791209571_3672a7bd31_o.jpg\" alt=\"Class 12 Important Questions for Maths -\u00a0Continuity and Differentiability\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Multiple Choice Questions<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/15794649982_a10b12f9fa_o.jpg\" alt=\"Class 12 Important Questions for Maths -\u00a0Continuity and Differentiability\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Fill In Blanks Type Questions<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/15607919377_947f86d9a5_o.jpg\" alt=\"Class 12 Important Questions for Maths -\u00a0Continuity and Differentiability\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">True or False Statements Type Questions<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/15791208891_3ac69d877e_o.jpg\" alt=\"Class 12 Important Questions for Maths -\u00a0Continuity and Differentiability\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Answers<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063522412_794d1a024c_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062794318_84637f676d_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49062794278_4f0f0c17ac_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2024\/05\/49063522327_8332c278b2_o.png\" alt=\"\"\/><\/figure>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/www.indcareer.com\/schools\/ncert-exemplar-problems-solutions\/\" style=\"background-color:#f06d6d\" target=\"_blank\" rel=\"noreferrer noopener\">NCERT Exemplar Solutions<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/www.indcareer.com\/schools\/ncert-exemplar-class-12-Maths-important-questions\/\" style=\"background-color:#f06d6d\" target=\"_blank\" rel=\"noreferrer noopener\">NCERT Class 12 Exemplar Solutions<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Exemplar Class 12 Maths Chapter 5: Continuity and Differentiability. NCERT Exemplar Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability prepare students for their Class 12 exams thoroughly. Maths problems and solutions for the Class 12 pdf are provided here which are similar to the questions being asked in the previous year&#8217;s board. [&hellip;]<\/p>\n","protected":false},"author":302,"featured_media":617906,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[1411,25],"tags":[],"boards":[],"class_list":["post-617904","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-book-solutions","category-class-12","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.0 (Yoast SEO v27.1.1) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Exemplar for Class 12, Maths Chapter 1 - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"NCERT Exemplar Class 12 Maths Chapter 5: Continuity and Differentiability | Browse all Class 12 Maths Chapters NCERT Exemplar books - IndCareer Schools\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.indcareer.com\/schools\/ncert-exemplar-class-12-maths-chapter-5-continuity-and-differentiability\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Exemplar Class 12 Maths Chapter 5: Continuity and Differentiability\" \/>\n<meta property=\"og:description\" content=\"NCERT Exemplar Class 12 Maths Chapter 5: Continuity and Differentiability. 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