{"id":1230,"date":"2021-12-17T18:02:42","date_gmt":"2021-12-17T12:32:42","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=1230"},"modified":"2025-06-03T17:34:35","modified_gmt":"2025-06-03T12:04:35","slug":"ncert-solutions-for-class-11-maths-chapter-13-limits-and-derivatives","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/chapter-13-limits-and-derivatives\/","title":{"rendered":"NCERT Solutions for Class 11 Maths Chapter 13: Limits and Derivatives"},"content":{"rendered":"<p><span data-contrast=\"auto\">Subject specialists have created NCERT Solutions for Class 11 Maths Chapter 13- Limits and Derivatives, which includes thorough solutions for reference. All of the questions from the textbook&#8217;s exercises are answered here. Students can use these answers to help them prepare for their exams. The <strong><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/\" target=\"_blank\" rel=\"noopener\">NCERT Solutions for Class 11<\/a><\/span><\/strong> provide useful solutions for improving conceptual knowledge.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:240,&quot;335559739&quot;:160,&quot;335559740&quot;:256}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving <strong><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/\" target=\"_blank\" rel=\"noopener\">NCERT Solutions for Class 11 Maths<\/a><\/span><\/strong>. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 11 pupils perform well in upcoming competitive exams.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:240,&quot;335559739&quot;:160,&quot;335559740&quot;:256}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:240,&quot;335559739&quot;:160,&quot;335559740&quot;:256}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">NCERT Solutions for Class 11 Maths Chapter 13- Limits and Derivatives<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559738&quot;:240,&quot;335559739&quot;:160,&quot;335559740&quot;:256}\"> <\/span><\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 100%;\"><span style=\"color: #0000ff;\">Exercise 13.1 Solutions<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;\"><span style=\"color: #0000ff;\">Exercise 13.2 Solutions<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/chapter-13-probability-miscellaneous-exercise\/\" target=\"_blank\" rel=\"noopener\">Miscellaneous Exercise Solutions<\/a><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\t\t<div class=\"download-pdf-container\">\n\t\t\t<span class=\"title\">Do you need help with your Homework? 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wpcf7-validates-as-required wpcf7-validates-as-number\" aria-required=\"true\" aria-invalid=\"false\" \/><\/span><\/p>\n<p><span style=\"display:none;\"><span class=\"wpcf7-form-control-wrap current-page-url\"><input type=\"text\" name=\"current-page-url\" value=\"https:\/\/_:443\/surge\/wp-json\/wp\/v2\/posts\/1230\" size=\"40\" class=\"wpcf7-form-control wpcf7dtx-dynamictext wpcf7-dynamictext\" aria-invalid=\"false\" \/><\/span><\/span><\/p>\n<style>.wpcf7-list-item{margin: 0 0.5em 0 0!important;}<\/style>\n<p class=\"title\" style=\"color: #6e6e6e;font-size:14px;font-weight:400;text-decoration: un;\"><span class=\"wpcf7-form-control-wrap acceptance-agreement\"><span class=\"wpcf7-form-control wpcf7-acceptance\"><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"acceptance-agreement\" value=\"1\" aria-invalid=\"false\" checked=\"checked\" \/><\/span><\/span><\/span> I agree to the <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/terms\" style=\"text-decoration: underline;\">terms and conditions<\/a> and <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/privacy\" style=\"text-decoration: underline;\">privacy policy<\/a>.<\/p>\n<p><input type=\"button\" style=\"cursor:pointer;width:auto;\" class=\"il_otp_submit\" value=\"Get OTP\" onclick=\"sendCF7OTP(this, otp_phone.value, user_name.value)\"><\/p>\n<div class=\"form-submit-btn-div\" style=\"display:none;\">\n<input type=\"submit\" value=\"Download PDF\" class=\"wpcf7-form-control has-spinner wpcf7-submit download-pdf-submit\" \/>\n<\/div>\n<\/div>\n<div class=\"wpcf7-response-output\" aria-hidden=\"true\"><\/div><\/form><\/div>\n\t\t\t\t\t<span class=\"pdf-link hidden\" data-pdf=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Maths_Class-11_Ch-13.pdf\"><\/span>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t<div class=\"bg-overlay\"><\/div>\n\t\t<\/div>\n\t\t<a href=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Maths_Class-11_Ch-13.pdf\" class=\"pdfemb-viewer\" style=\"\" data-width=\"max\" data-height=\"max\" data-mobile-width=\"0\"  data-scrollbar=\"both\" data-download=\"off\" data-tracking=\"on\" data-newwindow=\"on\" data-pagetextbox=\"off\" data-scrolltotop=\"on\" data-startzoom=\"100\" data-startfpzoom=\"100\" data-toolbar=\"top\" data-toolbar-fixed=\"on\">Maths Class 11_Ch 13<br\/><\/a>\n<p><b><span data-contrast=\"none\">NCERT Solutions for Class 11 Maths Chapter 13 \u2013 Limits and Derivatives<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559738&quot;:300,&quot;335559739&quot;:160,&quot;335559740&quot;:264}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Chapter 13 of Maths for Class 11 Limits and derivatives are covered individually in CBSE Syllabus 2021-22 as Limits in the term I and Derivatives in term II, and contain the following:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">13.1 Introduction<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">This section introduces the calculus, derivative, limits, and algebra of limits branches of mathematics. Certain standard functions&#8217; derivatives are also examined.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:240,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<ul>\n<li><span data-contrast=\"none\">In electrical engineering, calculus is used to determine the length of wire to be used between two stations that are kilometers apart.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"none\">Calculus is used to determine an object&#8217;s velocity and trajectory.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"none\">In operations research, calculus is utilized to increase efficiency, productivity, and profit.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559739&quot;:240,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<\/ul>\n<p><b><span data-contrast=\"none\">13.2 Intuitive Idea of Derivatives<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">This section explains how to calculate the derivative of a function using a real-life example of distance traveled at various time intervals.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The derivative refers to the pace at which one quantity changes in relation to another. If you run a business (for example, selling sweets), derivatives can assist you to figure out how much to sell. Data on your company&#8217;s performance over the previous few months should be collected, and the trend should be assessed by plotting a curve. The instantaneous slope (dy\/dx) of this graph is defined by derivative.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The slope indicates the marginal cost of generating each extra unit at that time (cost change\/unit produced change). If this cost exceeds the selling price of ten dollars, a loss is incurred at this moment.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Refer to the table given below, for a better understanding:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">For 0-300 units, if the cost &gt; sales, then it\u2019s a loss<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">For 400-600 units, if the sales &gt; cost, then it\u2019s a profit<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">13.3 Limits<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">This part teaches limitations with an engaging example, as well as the left-hand and right-hand limits, as well as solved issues.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">When an ice cube is thrown into a glass of warm water and the temperature is recorded over time, it represents a limit as time approaches infinity. The temperature steadily reaches the room temperature where the glass was stored during the time period monitored.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">13.3.1 Algebra of limits<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The output of the sum, difference, product, and quotient of limits is shown in this section.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">13.3.2 Limits of polynomials and rational functions<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The limits of polynomials and rational functions are discussed in detail, with examples provided.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">13.4 Limits of Trigonometric Functions<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">This section covers function theorems and prepositions, which are useful in determining the limits of several trigonometric functions.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">13.5 Derivatives<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">This section assists students in locating answers to various derivative problems.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Money-related institutions must anticipate changes in the assessment of certain stocks based on their current value. In this situation, as well as many others, it&#8217;s critical to understand how one parameter changes in relation to another. The derivative of a function at a given point in its domain of definition lies at the heart of the book.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">13.5.1 Algebra of derivatives of functions<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The result of sum, difference, product, and quotient of derivatives is shown in this section.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">13.5.2 Derivative of polynomials and trigonometric functions<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Theorems and problems for functions that help compute the derivatives of several trigonometric functions are covered in this section.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p aria-level=\"2\"><b><span data-contrast=\"none\">Following are the concepts discussed in Chapter 13 Limits and Derivatives:<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559738&quot;:300,&quot;335559739&quot;:160,&quot;335559740&quot;:264}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\u25cf\" data-font=\"Roboto\" data-listid=\"1\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"none\">The function&#8217;s expected value, as determined by the points to the left of a point, determines the function&#8217;s left-hand limit at that point. The right-hand limit is similar.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li data-leveltext=\"\u25cf\" data-font=\"Roboto\" data-listid=\"1\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"none\">The common value of the left and right-hand limits if they coincide is the limit of a function at a location.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li data-leveltext=\"\u25cf\" data-font=\"Roboto\" data-listid=\"1\" aria-setsize=\"-1\" data-aria-posinset=\"3\" data-aria-level=\"1\"><span data-contrast=\"none\">For a function f and a real number, a lim x \u2192 a f(x) and f (a) may not be the same.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559739&quot;:240,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<\/ul>\n<p><span data-contrast=\"none\">The PDF solutions include a detailed explanation for each problem. Limits and Derivatives NCERT Solutions for Class 11 Maths Chapter 13 are at your fingertips. The solutions are designed so that a student understands the split-up marks for each segment, allowing them to determine how much time and effort they should devote to each section of the first and second-term exams. The NCERT Solutions have been recommended by high-scoring students as a good source of information on each topic.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p aria-level=\"2\"><strong>Frequently Asked Questions on NCERT Solutions for Class 11 Maths Chapter 13<\/strong><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559738&quot;:300,&quot;335559739&quot;:620,&quot;335559740&quot;:264}\"> <\/span><\/p>\n<ol>\n<li aria-level=\"2\"><span style=\"color: #ff0000;\">What is the effective way to study Chapter 13 of NCERT Solutions for Class 11 Maths? <\/span><\/li>\n<li aria-level=\"2\"><span style=\"color: #ff0000;\">Can I get the NCERT Solutions for Class 11 Maths Chapter 13 in PDF format? <\/span><\/li>\n<li aria-level=\"2\"><span style=\"color: #ff0000;\" data-contrast=\"none\">Explain the difference between integral calculus and differential calculus as per Chapter 13 of NCERT Solutions for Class 11 Maths?<\/span><\/li>\n<\/ol>\n<p aria-level=\"3\"><strong>1. What is the effective way to study Chapter 13 of NCERT Solutions for Class 11 Maths? <\/strong><\/p>\n<p><span data-contrast=\"none\">Chapter 13 Limits and Derivatives questions and solutions are crucial in laying a solid foundation of key concepts. The actions listed below should be performed in order to successfully cover the concepts:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:460,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<ol>\n<li><span data-contrast=\"none\"> Review the fundamental ideas<\/span><\/li>\n<li><span data-contrast=\"none\"> Recognize whether the topic is integral or differential calculus.<\/span><\/li>\n<li><span data-contrast=\"none\"> Memorize the key formulas.<\/span><\/li>\n<li><span data-contrast=\"none\"> Recognize your limitations<\/span><\/li>\n<li><span data-contrast=\"none\"> Understand the calculus fundamental theorem.<\/span><\/li>\n<li><span data-contrast=\"none\"> Make it a habit to practice the issues on a daily basis.<\/span><\/li>\n<\/ol>\n<p aria-level=\"3\"><strong>2. Can I get the NCERT Solutions for Class 11 Maths Chapter 13 in PDF format? <\/strong><\/p>\n<p><span data-contrast=\"none\">Yes, students can access the NCERT Solutions for Class 11 Maths Chapter 13 in \u2018INFINITY learn\u2019 in PDF format. The solutions for the exercise-by-exercise difficulties are created by highly experienced faculty using the most up-to-date CBSE Syllabus for each term. Students can also compare their answers to the solutions PDF to acquire a better understanding of the alternative approaches for tackling complicated issues quickly.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:460,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p aria-level=\"3\"><strong>3. Explain the difference between integral calculus and differential calculus as per Chapter 13 of NCERT Solutions for Class 11 Maths?<\/strong><\/p>\n<p><span data-contrast=\"none\">Differential calculus uses functional derivatives to calculate the rate of change of a variety of values across time. Integral calculus deals with antiderivatives and is the polar opposite of differential calculus. Students should keep this idea in mind as they study this chapter since it will help them learn the principles more quickly.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:460,&quot;335559740&quot;:276}\"> <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Subject specialists have created NCERT Solutions for Class 11 Maths Chapter 13- Limits and Derivatives, which includes thorough solutions for [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"NCERT Solutions for Class 11 Maths Chapter 13","_yoast_wpseo_title":"NCERT Solutions for Class 11 Maths Chapter 13","_yoast_wpseo_metadesc":"NCERT solutions of Chapter 13: Limits and Derivatives Exercise Questions with Solutions to help you to revise the complete 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