# NCERT Solutions Class 12 Mathematics Chapter 5 Continuity and Differentiability

## Chapter 5 Continuity and Differentiability Class 12 Mathematics NCERT Solutions

Class 12 Mathematics students should refer to the following NCERT questions with answers for Chapter 5 Continuity and Differentiability in Class 12. These NCERT Solutions with answers for Class 12 Mathematics will come in exams and help you to score good marks

### Chapter 5 Continuity and Differentiability NCERT Solutions Class 12 Mathematics

Exercise 5.1

Question. Prove that the function f (x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.

The given function is f(x) = 5x - 3
At x = 0, f(0) = 5× 0 -3 = -3

Question. Examine the continuity of the function f (x) = 2x2 – 1 at x = 3.

The given function is f(x) = 2x2 - 1

Question. Examine the following functions for continuity.
(i) f(x) = x - 5
(ii) f(x) = [1/(x- 5)] , x ≠ 5
(iii) f(x) = (x2 - 25)/(x + 5), x ≠ - 5
(iv) f(x) = |x - 5|, x ≠ 5

(i) The given function is f(x) = x - 5
It is evident that f is defined at every real number k and its value at k is k - 5 .
It is also observed that

Hence, f is continuous at every real number and therefore, it is a continuous function.

(ii) The given function is f(x) =  [1/(x- 5)] , x ≠ 5
For any real number k ≠ 5, we obtain

Hence, f is continuous at every point in the domain of f and therefore, it is a continuous function.

(iii) The given function is f(x) = (x2 - 25)/(x + 5), x ≠ - 5
For any real number c ≠ - 5 , we obtain

Hence, f is continuous at every point in the domain of f and therefore, it is a continuous function.

Therefore, f is continuous at all real numbers greater than 5.
Hence, f is continuous at every real number and therefore, it is a continuous function

Question. Prove that the function f(x) = xn is continuous at x = n, where n is a positive integer.

The given function is f(x) = xn
It is evident that f is defined at all positive integers, n, and its value at n is nn .

Question. Is the function f defined by f(x) =

continuous at x = 0? At x = 1? At x = 2?

Question. Find all points of discontinuity of f,  where f is defined by

It is evident that the given function f is defined at all the points of the real line.
Let c be a point on the real line. Then, three cases arise.
c < 2
c > 2
c = 2
Case I : c < 2
f(c) = 2c + 3
Then,

It is observed that the left and right hand limit of f at x = 2 do not coincide.
Therefore, f is not continuous at x = 2 .
Hence, x = 2 is the only point of discontinuity of f.

 NCERT Solutions Class 12 Mathematics Chapter 1 Relations and Functions
 NCERT Solutions Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions
 NCERT Solutions Class 12 Mathematics Chapter 3 Matrices
 NCERT Solutions Class 12 Mathematics Chapter 4 Determinants
 NCERT Solutions Class 12 Mathematics Chapter 5 Continuity and Differentiability
 NCERT Solutions Class 12 Mathematics Chapter 6 Application of Derivatives
 NCERT Solutions Class 12 Mathematics Chapter 7 Integrals
 NCERT Solutions Class 12 Mathematics Chapter 8 Application of Integrals
 NCERT Solutions Class 12 Mathematics Chapter 9 Differential Equations
 NCERT Solutions Class 12 Mathematics Chapter 10 Vector Algebra
 NCERT Solutions Class 12 Mathematics Chapter 11 Three Dimensional Geometry
 NCERT Solutions Class 12 Mathematics Chapter 12 Linear Programming
 NCERT Solutions Class 12 Mathematics Chapter 13 Probability

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### NCERT Solutions Class 12 Mathematics Chapter 5 Continuity and Differentiability

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### Chapter 5 Continuity and Differentiability Class 12 Mathematics NCERT Solutions

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#### NCERT Solutions Chapter 5 Continuity and Differentiability Class 12 Mathematics

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#### Chapter 5 Continuity and Differentiability Class 12 NCERT Solution Mathematics

These solutions of Chapter 5 Continuity and Differentiability NCERT Questions given in your textbook for Class 12 Mathematics have been designed to help students understand the difficult topics of Mathematics in an easy manner. These will also help to build a strong foundation in the Mathematics. There is a combination of theoretical and practical questions relating to all chapters in Mathematics to check the overall learning of the students of Class 12.

#### Class 12 NCERT Solution Mathematics Chapter 5 Continuity and Differentiability

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