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# NCERT Exemplar Class 11 Maths Chapter 13 Solutions: Limits and Derivatives

NCERT Exemplar Solutions for Class 11 Maths Chapter 13 is an introduction to a very important area known as Calculus. It is that division of Maths which is linked to the study of change in the value of a function as the facts of the domain change. Some of the main topics included in the exemplar problems of the chapter of NCERT Exemplar Class 11 Science are limits of a function, limits of trigonometric functions, algebra of derivatives of functions, some properties of limits, limits of polynomials and rational functions, and derivatives.

Chapter 13 – Limits and Derivatives consists of 5 exercises with a total of 108 exemplar questions. Solving these exemplar problems will help you to clarify your doubts and offer a strong foundation for every concept. It is an important chapter in Maths. So, these books are widely used to excel in your exams as it provides a huge number of questions to practice.

With the help of NCERT Exemplar Class 11 Maths Problems and Solutions of Chapter 13, you should be capable of solving the complex problem in each exercise. Also, the main advantage of referring to these study materials is that they are prepared by the experts at Instasolv as per the CBSE syllabus. These solutions will also help you prepare for JEE Main, JEE Advanced, and other entrance exams.

## Important Topics for NCERT Maths Exemplar Solutions Class 11 Chapter 13 – Limits and Derivatives

Types of Limits:

Generally, there are two types of limits available including right-hand limit and left-hand limit.

• Right-hand Limit: Value of f(x) which is read out by values of f(x) when x inclines to from the right.
• Left-hand Limit: Value of f(x) which is read out by values of f(x) when x inclines to from the left.

Important Formulas of Limits and Derivatives

There are various operations for functions f and g which are provided below:

• limit (xm) [f (x) ± g (x)] = limit (xm) f (x) ± limit (xm) g (x)
• limit (xm) [f (x). g (x)] = limit (xm) f (x). limit (xm) g (x)
• limit (xm) [f (x)/ g (x)] = limit (xm) f (x) / limit (xm) g (x)

Standard limits:

• limit (xm) where [(x n – m n )/ (x – m) = n a (n-1)
• limit (x 0) where [sin x/ x] = 1
• limit (x 0) where [1 – cos x/ x] = 0

Derivative of a function ‘f’ at m can be denoted as-

F’ (a) = limit (z 0) [{f (m + z) – f (m)}/ z]

Derivative of a function f at x can be denoted as-

F’ (x) = limit (z 0) [{f (x + z) – f (x)}/ z]

For functions u and v, use the following equations:

• (u ± v)’ = u’ ±  v’
• (uv)’ = u’v + uv’
• (u/v)’ = u’v – uv’/ v2

### Exercise Discussion of NCERT Maths Exemplar Solutions Class 11 Chapter 13 – Limits and Derivatives

The solutions of NCERT Exemplar Class 11 for Maths Chapter 13 consists of 28 solved examples for your reference to practice the exercises with ease. Other than this, there are 5 main exercises in the chapter. It has a total of around 108 questions. The detailed description of all these exercises are listed below:

Exercise 13.1 – Short Answer Type Questions

In this exercise of Chapter 13 – Limits and Derivatives there are a total of 42 questions that are based on the concepts of limits of a function and limits of trigonometric functions.

Exercise 13.2 – Long Answer Type Questions

NCERT Exemplar Problems Class 11 Maths Solutions for Chapter 13 Exercise 13.2 contains a total of 11 questions. They are long answer type questions where you have to find the algebra of derivatives of functions, some properties of limits, limits of polynomials and rational functions, and derivatives.

Exercise 13.3 – Objective Type Questions

This exercise consists of a total of 23 questions which are objective type questions based on the limits of trigonometric functions and some important formulae. In this exercise, you will find 4 options in each question. Out of them, you have to choose the right answer.

Exercise 4 and 5 consists of very short answer type questions including fill in the blanks, match the following and state true or false type questions.

## Why Use NCERT Maths Exemplar Solutions Class 11 Chapter 13 – Limits and Derivatives by Instasolv?

• Along with the exemplar solutions for Class 11 Maths Chapter 13 – Limits and Derivatives, Instasolv provides access to NCERT Exemplar Problems for all chapters of CBSE Class 11 Maths as well.
• One of the main advantages of our solutions is that we cover all the questions and sub-questions of the exercises that can be accessed anywhere and anytime.
• Our experts have prepared the solutions to present the complex topics of Chapter 13 in the simplest manner.
• The solutions offered by Instasolv are updated regularly, which is to the point, detailed and at the same time provides an in-depth overview of the chapter.
• You can access the NCERT Maths Exemplar Solutions for ‘Limits and Derivatives’ Chapter for FREE!
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