{"id":56210,"date":"2021-05-19T16:26:00","date_gmt":"2021-05-19T10:56:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=56210"},"modified":"2023-05-10T17:56:25","modified_gmt":"2023-05-10T12:26:25","slug":"ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability"},"content":{"rendered":"\n<p><strong>NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability<\/strong> presents explanations to all of the questions posed in the chapter (All Exercises and Miscellaneous Exercise Solutions). This Continuity and Differentiability NCERT Solutions have been expertly documented and created in accordance with the most recent <a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-12-maths-syllabus\/\"><strong>CBSE Maths syllabus<\/strong><\/a>.<\/p>\n<ul>\n<li><strong>All you need to know about\u00a0<a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-12-maths-ncert-solutions\/\" target=\"_blank\" rel=\"noopener noreferrer\">NCERT Solutions For Class 12 Maths<\/a><\/strong><\/li>\n<\/ul>\n<p>Subject experts address all of the NCERT <a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-12-maths\/\"><strong>Class 12 Maths<\/strong><\/a> questions. These Chapter 5 Maths Class 12 can be downloaded by students to improve their basics. Therefore we are here to provide NCERT Solutions for Class 12 Maths Chapter 5.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69d39f960ff6a\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69d39f960ff6a\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#download-ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability-pdf\" title=\"Download NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability PDF\">Download NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#what-will-you-gain-in-cbse-class-12-maths-chapter-5-%e2%80%93-continuity-and-differentiability\" title=\"What will you gain in CBSE Class 12 Maths Chapter 5 &#8211; Continuity and Differentiability?\">What will you gain in CBSE Class 12 Maths Chapter 5 &#8211; Continuity and Differentiability?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#ncert-solutions-for-class-12-maths-chapter-5-exercise-51\" title=\"NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.1\">NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#ncert-solutions-for-class-12-maths-chapter-5-exercise-52\" title=\"NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.2\">NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#ncert-solutions-for-class-12-maths-chapter-5-exercise-53\" title=\"NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.3\">NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#continuity-and-differentiability-class-12-ncert-solutions-exercise-54\" title=\"Continuity and Differentiability Class 12 NCERT Solutions Exercise 5.4\">Continuity and Differentiability Class 12 NCERT Solutions Exercise 5.4<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#continuity-and-differentiability-class-12-ncert-solutions-exercise-55\" title=\"Continuity and Differentiability Class 12 NCERT Solutions Exercise 5.5\">Continuity and Differentiability Class 12 NCERT Solutions Exercise 5.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#continuity-and-differentiability-class-12-ncert-solutions-exercise-56\" title=\"Continuity and Differentiability Class 12 NCERT Solutions Exercise 5.6\">Continuity and Differentiability Class 12 NCERT Solutions Exercise 5.6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#chapter-5-maths-class-12-ncert-solutions-exercise-57\" title=\"Chapter 5 Maths Class 12 NCERT Solutions Exercise 5.7\">Chapter 5 Maths Class 12 NCERT Solutions Exercise 5.7<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#chapter-5-maths-class-12-ncert-solutions-exercise-58\" title=\"Chapter 5 Maths Class 12 NCERT Solutions Exercise 5.8\">Chapter 5 Maths Class 12 NCERT Solutions Exercise 5.8<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#chapter-5-maths-class-12-formulas-and-theorems\" title=\"Chapter 5 Maths Class 12 Formulas and Theorems\u00a0\">Chapter 5 Maths Class 12 Formulas and Theorems\u00a0<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#go-through-class-12-maths-continuity-and-differentiability-formulas-and-theorems\" title=\"Go through Class 12 Maths Continuity and Differentiability formulas and theorems:\">Go through Class 12 Maths Continuity and Differentiability formulas and theorems:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#definition-of-continuity\" title=\"Definition of Continuity:\">Definition of Continuity:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#also-access\" title=\"Also Access:\">Also Access:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#benefits-of-ncert-solutions-for-class-12-maths-chapter-5\" title=\"Benefits of NCERT Solutions for Class 12 Maths Chapter 5\">Benefits of NCERT Solutions for Class 12 Maths Chapter 5<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#faqs-ncert-solutions-for-class-12-maths-chapter-5\" title=\"FAQs: NCERT Solutions for Class 12 Maths Chapter 5\">FAQs: NCERT Solutions for Class 12 Maths Chapter 5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#how-many-exercises-are-there-in-chapter-5-of-the-ncert-textbook-for-class-12-maths\" title=\"How many exercises are there in Chapter 5 of the NCERT textbook for Class 12 Maths?\">How many exercises are there in Chapter 5 of the NCERT textbook for Class 12 Maths?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#where-can-i-get-maths-chapter-5-class-12-ncert-solutions\" title=\"Where can I get Maths Chapter 5 Class 12 NCERT solutions?\">Where can I get Maths Chapter 5 Class 12 NCERT solutions?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#are-ncert-solutions-class-12-maths-chapter-5-helpful\" title=\"Are NCERT Solutions Class 12 Maths Chapter 5 helpful?\">Are NCERT Solutions Class 12 Maths Chapter 5 helpful?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#can-i-receive-an-overview-of-the-ncert-solutions-for-class-12-maths-chapter-5-exercises\" title=\"Can I receive an overview of the NCERT Solutions for Class 12 Maths Chapter 5 exercises?\">Can I receive an overview of the NCERT Solutions for Class 12 Maths Chapter 5 exercises?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/#are-continuity-class-12-ncert-solutions-enough-for-board-examination-preparation\" title=\"Are Continuity Class 12 NCERT Solutions enough for board examination preparation?\">Are Continuity Class 12 NCERT Solutions enough for board examination preparation?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability-pdf\"><\/span><strong>Download NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability PDF<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Go through our Class 12 Maths Chapter 5 NCERT Solutions:<\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2020\/10\/Class-12-Mathematics-Solutions-Chapter-5-1.pdf\">Class-12-Mathematics-Solutions-Chapter-5 pdf<\/a><\/p>\n<p>\u00a0<\/p>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2020\/10\/Class-12-Mathematics-Solutions-Chapter-5-1.pdf\", \"#example1\");<\/script><\/p>\n<p>Practicing these <strong>Class 12 Maths Continuity and Differentiability NCERT Solutions<\/strong> will aid you in the <a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-12-board-exam\/\"><strong>12th board exam<\/strong><\/a> preparation in such a way that even the most difficult questions from this chapter will appear to be simple. Scroll down to know more!<\/p>\n<h2><span class=\"ez-toc-section\" id=\"what-will-you-gain-in-cbse-class-12-maths-chapter-5-%e2%80%93-continuity-and-differentiability\"><\/span><strong>What will you gain in CBSE Class 12 Maths Chapter 5 &#8211; Continuity and Differentiability?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The chapter comes packed with 8 exercises along with miscellaneous exercises thus including all the essential elements associated with the topic. Let us check the subtopic covered in this chapter now-<\/p>\n<table style=\"width: 100%; height: 972px;\" width=\"624\">\n<tbody>\n<tr style=\"height: 108px;\">\n<td style=\"height: 108px;\" width=\"84\">\n<p>5.1<\/p>\n<\/td>\n<td style=\"height: 108px;\" width=\"540\">\n<p>Introduction<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 108px;\">\n<td style=\"height: 108px;\" width=\"84\">\n<p>5.2<\/p>\n<\/td>\n<td style=\"height: 108px;\" width=\"540\">\n<p>Continuity<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 108px;\">\n<td style=\"height: 108px;\" width=\"84\">\n<p>5.3<\/p>\n<\/td>\n<td style=\"height: 108px;\" width=\"540\">\n<p>Differentiability<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 108px;\">\n<td style=\"height: 108px;\" width=\"84\">\n<p>5.4<\/p>\n<\/td>\n<td style=\"height: 108px;\" width=\"540\">\n<p>Exponential and Logarithmic Functions<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 108px;\">\n<td style=\"height: 108px;\" width=\"84\">\n<p>5.5<\/p>\n<\/td>\n<td style=\"height: 108px;\" width=\"540\">\n<p>Logarithmic Differentiation<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 108px;\">\n<td style=\"height: 108px;\" width=\"84\">\n<p>5.6<\/p>\n<\/td>\n<td style=\"height: 108px;\" width=\"540\">\n<p>Derivatives of Functions in Parametric Forms<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 108px;\">\n<td style=\"height: 108px;\" width=\"84\">\n<p>5.7<\/p>\n<\/td>\n<td style=\"height: 108px;\" width=\"540\">\n<p>Second-Order Derivative<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 108px;\">\n<td style=\"height: 108px;\" width=\"84\">\n<p>5.8<\/p>\n<\/td>\n<td style=\"height: 108px;\" width=\"540\">\n<p>Mean Value Theorem<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 108px;\">\n<td style=\"height: 108px;\" width=\"84\">\n<p>Others<\/p>\n<\/td>\n<td style=\"height: 108px;\" width=\"540\">\n<p>Miscellaneous Q&amp;A<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Let us now have a quick look at the NCERT Solutions for Class 12 Maths Chapter 5 exercises of the chapter-<\/strong><\/p>\n<table width=\"624\">\n<tbody>\n<tr>\n<td width=\"312\">\n<p>Exercise 5.1 Solutions<\/p>\n<\/td>\n<td width=\"312\">\n<p>34 Questions (Short Answers)<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">\n<p>Exercise 5.2 Solutions<\/p>\n<\/td>\n<td width=\"312\">\n<p>10 Questions(Short Answers)<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">\n<p>Exercise 5.3 Solutions<\/p>\n<\/td>\n<td width=\"312\">\n<p>15 Questions ( Short Answers)<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">\n<p>Exercise 5.4 Solutions<\/p>\n<\/td>\n<td width=\"312\">\n<p>10 Questions (Short Answers)<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">\n<p>Exercise 5.5 Solutions<\/p>\n<\/td>\n<td width=\"312\">\n<p>18 Questions ( Short Answers)<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">\n<p>Exercise 5.6 Solutions<\/p>\n<\/td>\n<td width=\"312\">\n<p>11 Questions (Short Answers)<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">\n<p>Exercise 5.7 Solutions<\/p>\n<\/td>\n<td width=\"312\">\n<p>17 Questions (Short Answers)<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">\n<p>Exercise 5.8 Solutions<\/p>\n<\/td>\n<td width=\"312\">\n<p>\u00a06 Questions (Short Answers)<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"312\">\n<p>Miscellaneous exercise Solutions<\/p>\n<\/td>\n<td width=\"312\">\n<p>23 Questions (6 Long, 17 Short)<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Students, let us now take a look at the content-<\/p>\n<h3><span class=\"ez-toc-section\" id=\"ncert-solutions-for-class-12-maths-chapter-5-exercise-51\"><\/span><strong>NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.1<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>With a proper introduction to the chapter, there begins the NCERT Solutions for Class 12 Maths Chapter 5 &#8211; Continuity and Differentiability. Though you have minute knowledge about the same from your previous class, however, this chapter will give complete closure to the concept.\u00a0<\/p>\n<p>This chapter also teaches differentiation between inverse trigonometric functions, exponential concept, and logarithmic functions, and robust techniques of logarithm by geometrically distinct conditions by differential calculus.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"ncert-solutions-for-class-12-maths-chapter-5-exercise-52\"><\/span><strong>NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.2<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>This section teaches formula associated with the intuitive concept of functions that works without any breaks. A function is basically a relationship in which every value of the independent variable is connected with a dependable variable.<\/p>\n<p>It also focuses on the algebra of continuous functions, analogous algebra of uninterrupted functions,\u00a0 and more. The chapter is loaded with important formulas and theories which will definitely be a need for upcoming endeavors.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"ncert-solutions-for-class-12-maths-chapter-5-exercise-53\"><\/span><strong>NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.3<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>This portion lets you go through vivid details about derivatives, a list of derivatives, theorems, and formulas to follow. Additionally, this section also teaches differentiable function is continuous, derivatives of composite functions, derivatives of implicit functions, inverses trigonometric functions, and chain rule of the theorem, along with various examples which lets you build a clear image of the chapter.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"continuity-and-differentiability-class-12-ncert-solutions-exercise-54\"><\/span><strong>Continuity and Differentiability Class 12 NCERT Solutions Exercise 5.4<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>This section includes the various Classes of functions, proof of the theorem, the definition of exponential functions, and logarithms. This chapter helps you build a crystal clear notion to secure solid marks from this section.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"continuity-and-differentiability-class-12-ncert-solutions-exercise-55\"><\/span><strong>Continuity and Differentiability Class 12 NCERT Solutions Exercise 5.5<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>This section will offer knowledge that will make it simple for students to evaluate particular Classes of functions. The chapter centers around examples which simply makes it practical in its approach.\u00a0<\/p>\n<h3><span class=\"ez-toc-section\" id=\"continuity-and-differentiability-class-12-ncert-solutions-exercise-56\"><\/span><strong>Continuity and Differentiability Class 12 NCERT Solutions Exercise 5.6<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>This section teaches about the relation between two variables which is neither implicit nor explicit. Students will be taught how to link the third variable where each of the two variables is separated by building a relationship between the first two variables. Students will also learn about the third variable and more in this section.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"chapter-5-maths-class-12-ncert-solutions-exercise-57\"><\/span><strong>Chapter 5 Maths Class 12 NCERT Solutions Exercise 5.7<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>This section is also equipped with various examples to make the concept sorted thus paving your path to secure a solid understanding of the formulas and theorems enlisted here.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"chapter-5-maths-class-12-ncert-solutions-exercise-58\"><\/span><strong>Chapter 5 Maths Class 12 NCERT Solutions Exercise 5.8<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>This section teaches the student how to state two fundamental results in calculus without proof,\u00a0 along with theorems and geometric interpretation. This section also covers the functionality of the mean value theorem and its relation to Rolle\u2019s Theorem. The chapter also includes lots of theories and formulas associated with the content to provide an in-depth concept of the topic.\u00a0<\/p>\n<h2><span class=\"ez-toc-section\" id=\"chapter-5-maths-class-12-formulas-and-theorems\"><\/span><strong>Chapter 5 Maths Class 12 Formulas and Theorems\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h4><span class=\"ez-toc-section\" id=\"go-through-class-12-maths-continuity-and-differentiability-formulas-and-theorems\"><\/span>Go through Class 12 Maths Continuity and Differentiability formulas and theorems:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"definition-of-continuity\"><\/span><strong>Definition of Continuity:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(i) <\/strong>The continuity of a real function (f) on a subset of the real numbers is defined when the function exists at point c and is given as-<\/p>\n<p>Lim<\/p>\n<p>x\u2192c<\/p>\n<p>f(x)=f(c)<\/p>\n<p><strong>(ii) <\/strong>A real function (f) is said to be continuous if it is continuous at every point in the domain of f.<\/p>\n<p>Consider a function f(x), and the function is said to be continuous at every point in [a, b] including the endpoints a and b.<\/p>\n<p>Continuity of \u201cf\u201d at a means,<\/p>\n<p>Lim<\/p>\n<p>x\u2192a<\/p>\n<p>f(x)=f(a)<\/p>\n<p>Continuity of \u201cf\u201d at b means,<\/p>\n<p>Lim<\/p>\n<p>x\u2192b<\/p>\n<p>f(x)=f(b)<\/p>\n<p><strong>Differentiability formula<\/strong><\/p>\n<p>Assume that if f is a real function and c is a point in its domain. The derivative of f at c is defined by 0<\/p>\n<p>The derivative of a function f at c is defined by-<\/p>\n<p>Lim<\/p>\n<p>h\u21920<\/p>\n<p>f(x+h)\u2013f(c)<\/p>\n<p>h<\/p>\n<p><strong>Theorem 1: Algebra of continuous functions:<\/strong><\/p>\n<p>If the two real functions say f and g, are continuous at a real number c, then<\/p>\n<p><strong>(i) f + g<\/strong> is continuous at x=c.<\/p>\n<p><strong>(ii) f \u2013 g<\/strong> is continuous at x=c.<\/p>\n<p><strong>(iii) f. g<\/strong> is continuous at x=c.<\/p>\n<p><strong>(iv)f\/g <\/strong>is continuous at x=c, (provided g(c) \u2260 0).<\/p>\n<p><strong>Theorem 2: <\/strong>\u00a0Suppose f and g are real-valued functions such that (f o g) is defined at c. If g is continuous at c and if f is continuous at g (c), then (f o g) is continuous at c.<\/p>\n<p><strong>Theorem 3:<\/strong> If a function f is differentiable at a point c, then it is also continuous at that point.<\/p>\n<p><strong>Theorem 4 (Chain Rule):<\/strong> Let f be a real-valued function that is a composite of two functions u and v; i.e., f = v o u.<\/p>\n<p>Suppose t = u(x) and if both dt\/dx and dv\/dt exist, we have df\/dx = (dv\/dt). (dt\/dx)<\/p>\n<p><strong>Theorem 5:<\/strong><\/p>\n<p>(1) The derivative of ex with respect to x is ex;\u00a0 i.e., d\/dx(ex) = ex.<\/p>\n<p>(2) The derivative of log x with respect to x is 1\/x.<\/p>\n<p>i.e., d\/dx(log x) =1\/x.<\/p>\n<p><strong>Theorem 6 (Rolle\u2019s Theorem):<\/strong> 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 some c in (a, b) such that f'(c) = 0.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"also-access\"><\/span><em><strong>Also Access:<\/strong><\/em><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"content-box-orange\">\n<ul>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-12-maths-sample-papers\/\"><strong>CBSE Class 12 Maths Sample Papers<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-12-maths-previous-year-papers\/\"><strong>CBSE Class 12 Maths Previous year Papers<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-12-maths-rd-sharma-solutions\/\"><strong>CBSE Class 12 Maths RD Sharma Solutions<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-12-maths-rs-aggarwal-solutions\/\"><strong>CBSE Class 12 Maths RS Aggarwal Solutions<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-12-maths-revision-notes\/\"><strong>CBSE Class 12 Maths Revision Notes<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-12-maths-formulas\/\"><strong>CBSE Class 12 Maths Chapters All Formulas<\/strong><\/a><\/li>\n<\/ul>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"benefits-of-ncert-solutions-for-class-12-maths-chapter-5\"><\/span><strong>Benefits of NCERT Solutions for Class 12 Maths Chapter 5<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are several important points that ultimately support opting for this guide. Let\u2019s check them out<strong>&#8211;<\/strong><\/p>\n<ol>\n<li>The easy language format is undoubtedly helping you in finishing chapter 5 much before time.\u00a0<\/li>\n<li>It provides you with a thorough understanding of difficult concepts.<\/li>\n<li>NCERT solutions follow the CBSE curriculum to a tee, and most board exam questions are drawn from them.<\/li>\n<li>The NCERT Solutions for Class 12 Maths Chapter 5 are written by experts, there is no need to doubt the authenticity.<\/li>\n<li>It can be readily accessible and free of charge on the internet.<\/li>\n<\/ol>\n<p><strong>Well, we have jotted down the <a href=\"https:\/\/cbse.nic.in\/\" target=\"_blank\" rel=\"noopener noreferrer\">CBSE<\/a> NCERT Solutions for Class 12 Maths Chapter 5 &#8211; Continuity and Differentiability here. Make sure to get to the chapter thoroughly for securing a satisfying scorecard. Feel free to ask any queries in the comment section below!<\/strong><\/p>\n<h3><span class=\"ez-toc-section\" id=\"faqs-ncert-solutions-for-class-12-maths-chapter-5\"><\/span><strong>FAQs: NCERT Solutions for Class 12 Maths Chapter 5<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1621409918027\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-many-exercises-are-there-in-chapter-5-of-the-ncert-textbook-for-class-12-maths\"><\/span>How many exercises are there in Chapter 5 of the NCERT textbook for Class 12 Maths?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>In total, there are eight exercises in Chapter 5 of Class 12 Maths.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1621409963894\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-get-maths-chapter-5-class-12-ncert-solutions\"><\/span>Where can I get Maths Chapter 5 Class 12 NCERT solutions?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can get NCERT Solutions for Class 12 Maths Chapter 5 from the above blog.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1621410036233\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"are-ncert-solutions-class-12-maths-chapter-5-helpful\"><\/span>Are NCERT Solutions Class 12 Maths Chapter 5 helpful?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, the NCERT Ch. 5 exercises are addressed by subject matter experts who have a thorough understanding of the key ideas, and every step is described in easy-to-understand language.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1621410077770\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-receive-an-overview-of-the-ncert-solutions-for-class-12-maths-chapter-5-exercises\"><\/span>Can I receive an overview of the NCERT Solutions for Class 12 Maths Chapter 5 exercises?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes. Go through the above blog for an overview of the NCERT Solutions for Class 12 Maths Chapter 5 exercises.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1621410126052\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"are-continuity-class-12-ncert-solutions-enough-for-board-examination-preparation\"><\/span>Are Continuity Class 12 NCERT Solutions enough for board examination preparation?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes. Continuity Class 12 NCERT Solutions covers all the topics of a matrix which is sufficient for board examination preparation.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability presents explanations to all of the questions posed in the chapter (All Exercises and Miscellaneous Exercise Solutions). This Continuity and Differentiability NCERT Solutions have been expertly documented and created in accordance with the most recent CBSE Maths syllabus. All you need to know about\u00a0NCERT &#8230; <a title=\"NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-5-continuity-and-differentiability\/\" aria-label=\"More on NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":90250,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2934,2917,73712,73413,2985,73410],"tags":[3041,73226,73225,3570,75043],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/56210"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/238"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=56210"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/56210\/revisions"}],"predecessor-version":[{"id":367964,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/56210\/revisions\/367964"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/90250"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=56210"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=56210"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=56210"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}