# NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives

## NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives

This chapter introduces an important area of mathematics called Calculus. Calculus is the branch of mathematics in which we deal with the study of change in the value of a function as the points in the domain change. In this chapter, we will learn about Limits and Derivatives in detail. There is a total of 2 exercises with 43 questions in them and 30 questions are given in the miscellaneous exercise. The NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives are solved and prepared by our maths experts. These NCERT solutions help students in their preparation of class 11 final examination and also in various competitive exams like JEE Main, VITEEE etc.

The NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives starts with an intuitive idea of derivative (without actually defining it). Then the chapter covers the definition of a limit and discusses some algebra of limits. Then we come back to the actual definition of derivative and study some basic algebra derivatives.  We also obtain derivatives of certain standard functions. In NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives, there are two exercises, the first exercise of this chapter deals with problems on limits and the second exercise deals with problems on derivatives.

Important points and formulas of NCERT Class 11 Maths Chapter 13 Limits and Derivatives-

• Limit of a function(f) at a point is the common value of the left-hand limits and right-hand limits if they coincide.
• For a function 'f' and a real number 'a'. $\dpi{100} \lim_{x\rightarrow a}\:f(x)$ and $\dpi{100} f(a)$ may not be the same (One may be defined and not the other one).
• For functions 'f' and 'g' the following properties holds:

$\dpi{100} \\\lim_{x\rightarrow a} [f(x)\pm g(x)]=\lim_{x\rightarrow a}f(x)\pm \lim_{x\rightarrow a}g(x)\\\:\:\:\\lim_{x\rightarrow a} [f(x). g(x)]=\lim_{x\rightarrow a}f(x). \lim_{x\rightarrow a}g(x)\\\:\:\:\\lim_{x\rightarrow a}[\frac{f(x)}{g(x)}]=\frac{\lim_{x\rightarrow a}f(x)}{\lim_{x\rightarrow a}g(x)}$

• Some of the standard limits are-

$\dpi{100} \\\lim_{x\rightarrow a}\frac{x^n-a^n}{x-a}=na^{n-1}\\\:\\lim_{x\rightarrow a}\frac{sin\: x}{x}=1\\\:\\lim_{x\rightarrow a}\frac{1-cos\: x}{x}=0$

• The derivative of a function 'f' at 'a' is defined by-

$\dpi{100} f^{'}=\lim_{h\rightarrow 0}\frac{f(a+h)-f(a)}{h}$

• Derivative of a function 'f' at any point 'x' is defined by-

$\dpi{100} f^{'}(x)=\frac{df(x)}{dx}=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

## Topics of NCERT Grade 11 Maths Chapter-13 Limits and Derivatives

13.1 Introduction

13.2 Intuitive Idea of Derivatives

13.3 Limits

13.4 Limits of Trigonometric Functions

13.5 Derivatives

## The complete Solutions of NCERT Class 11 Mathematics Chapter 13 is provided below:

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives - Exercise 13.1

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives - Exercise 13.2

NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives - Miscellaneous

## NCERT Solutions for Class 11 Mathematics- Chapter-Wise

 Chapter-1 Chapter-2 Chapter-3 Chapter-4 Chapter-5 Chapter-6 Chapter-7 Chapter-8 Chapter-9 Chapter-10 Chapter-11 Chapter-12 Chapter-14 Chapter-15 Chapter-16

## NCERT Solutions for Class 11- Subject wise

 NCERT Solutions for Class 11 Biology NCERT Solutions for Class 11 Maths NCERT Solutions for Class 11 Chemistry NCERT Solutions for Class 11 Physics