Chapter 13 Limits and Derivatives

Introduced to 11th-grade students in Chapter 13, Limits and Derivatives, calculus is used in many complex sciences and engineering projects, from space flight to nuclear reactors. Students are required to complete the NCERT questions in Chapter 13 to better understand this complex topic. We have provided a detailed NCERT Class 11 Math Chapter 13 PDF step-by-step notes to help students solve problems from limits and derivatives. Notes are provided in a downloadable format for students to use offline. Read on to learn more about limits and derivatives and to find the download link for the NCERT notes for math 11th-grade chapter 13.

MATHEMATICS NOTES CHAPTER-13

Points to Remember

• In general as x → a, f(x) → l, then l is called limit of the function f(x) Symbolically written as For all the limits, function should assume at a given point x = a The two ways x could approach a number an either from left or from right, i.e., all the values of x near a could be less than a or could be greater than a.

Limits Representation

To express the limit of a function, we represent it as:

limn→cf(n)=L

Limits Formula

The following are the important limits formulas:

Limits of Important Trigonometric Functions:

• limx→0sinx=0

• limx→0cosx=1

• limx→01−cosxx=0

• limx→0sin−1xx=1

• limx→0tan−1xx=1

• limx→0sinxx=1

• limx→0tanxx=1

L’hospital’s Rule:

limx→af(x)g(x)=f′(a)g′(a)

, if

limx→af(x)g(x)

gives the form 0/0.

Where, f(a)=0 and g(a)=0.

Limits of Exponential and Log Functions:

• limx→0ex=1

• limx→0ex−1x=1

• limx→∞(1+1x)x=e

• limx→∞(1+ax)x=ea

• limx→0(1+x)1x=e

• limx→0ax−1x=logea

• limx→0log(1+x)x=1

Xn Formula:

limx→axn−anx−a=n(a)n−1

How to Check If Limit Exists?

To check whether the limit exists for the function f(x) at x=a,

We have to check, if

Left hand side limit = Right Hand side limit = f(A)

(i.e.),

limx→a−f(x)=limx→a+f(x)=f(a)

Properties of Limits

Let p and q be two functions and a be a value such that 

limx→ap(x)

and 

limx→aq(x)

exists.

Derivatives of a Function

A derivative refers to the instantaneous rate of change of a quantity with respect to the other. It helps to investigate the moment by moment nature of an amount. The derivative of a function is represented in the below-given formula.

Derivative Formula

limh→0f(x+h)−f(x)h

For the function f, its derivative is said to be f'(x) given the equation above exists. Check out all the derivative formulas here related to trigonometric functions, inverse functions, hyperbolic functions, etc.

Properties of Derivatives

Some of the important properties of derivatives are given below:

Topics and Sub-topics

The NCERT notes was developed by qualified and experienced scientists based on the recent 2021-2022 CBSE Curriculum Update. We will try to collect the amount of money you can think of in this topic when solving them. The focus is on students preparing for this chapter. Students are encouraged to solve all questions and clear all concepts in the NCERT book. This chapter asks questions about admissions tests such as JEE Main, BITSAT and other state CET. Provides a fully resolved NCERT notes for Grade 11 Math Chapter 13 from the best Vidyakul teachers.

NCERT Class 11 Mathematics Chapter 13 Straight Topics and Subtopics will help prepare you for CBSE Class 11 Mathematics. Topics and subtopics in this topic will help you prepare well for the CBSE exam. It will also help you understand the topics of NCERT Class 11 Maths Chapter 13.

13.1	Introduction
13.2	Intuitive Idea of Derivatives
13.3	Limits
13.3.1	Algebra of Limits
13.3.2	Limits of Polynomials and Rational Functions
13.4	Limits of Trigonometric Functions
13.5	Derivatives
13.5.1	Algebra of Derivative of Functions
13.5.2	Derivative of Polynomials and Trigonometric Functions

 

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