# NCERT Solutions for Class 12 Maths Continuity and Differentiability

Hi Students, Welcome to **Amans Maths Blogs (AMB)**. In this post, you will get the * NCERT Solutions for Class 12 Maths Continuity and Differentiability Exercise 5.1*. This

**can be downloaded in PDF file. The downloading link is given at last.**

*NCERT Solutions** CBSE Class 12^{th}* is an important school class in your life as you take some serious decision about your career. And out of all subjects, Maths is an important and core subjects. So

*is major role in your exam preparation as it has detailed chapter wise solutions for all exercise.*

**CBSE NCERT Solutions for Class 12**^{th}Maths* NCERT Solutions for Class 12 Maths* are not only the solutions of Maths exercise but it builds your foundation of other important subjects. Getting knowledge of depth concept of

*like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.*

**CBSE Class 12**^{th}MathsAs we know that all the schools affiliated from CBSE follow the NCERT books for all subjects. You can check the **CBSE NCERT Syllabus**. Thus, * NCERT Solutions* helps the students to solve the exercise questions as given in

*.*

**NCERT Books**## NCERT Solutions for Class 12 Maths Continuity and Differentiability Exercise 5.1

**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 1.**

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

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 2.**

Examine the continuity of the function f (x) = 2x^{2} – 1 at x = 3.

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 3.**

Examine the following functions for continuity.

(a) f (x) = x – 5

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(b) f (x) = 1 / (x – 5)

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(c) f (x) = (x^{2} – 25) / (x + 5)

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(d) f (x) = | x – 5 |

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 4.**

Prove that the function f (x) = x^{n} is continuous at x = n, where n is a positive integer.

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 5.**

Is the function f defined by continuous at x = 0? At x = 1? At x = 2?

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

**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 6.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 7.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 8.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 9.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 10.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 11.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 12.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 13.**

Is the function defined by a continuous function?

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Discuss the continuity of the function f, where f is defined by

**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 14.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 15.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 16.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 17.**

Find the relationship between a and b so that the function f defined by is continuous at x = 3.

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 18.**

For what value of λ is the function defined by continuous at x = 0? What about continuity at x = 1?

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 19.**

Show that the function defined by g (x) = x – [x] is discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x.

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 20.**

Is the function defined by f (x) = x^{2} – sin x + 5 continuous at x = π?

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 21.**

Discuss the continuity of the following functions:

(a) f (x) = sin x + cos x

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(b) f (x) = sin x – cos x

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(c) f (x) = sin x . cos x

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 22.**

Discuss the continuity of the cosine, cosecant, secant and cotangent functions.

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 23.**

Find all points of discontinuity of f, where

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 24.**

Determine if f defined by is a continuous function?

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 25.**

Examine the continuity of f, where f is defined by

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Find the values of k so that the function f is continuous at the indicated point in Exercises 26 to 29.

**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 26.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 27.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 28.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 29.**

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 30.**

Find the values of a and b such that the function defined by is a continuous function.

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 31.**

Show that the function defined by f (x) = cos (x^{2}) is a continuous function.

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**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 32.**

Show that the function defined by f (x) = | cos x | is a continuous function.

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We know that cosine function is every where continuous and also modulus function is continuous. Thus, |cos x| is continuous everywhere.

**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 33.**

Examine that sin | x | is a continuous function

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Let f(x) = |x| and g(x) = sin x. Then, (gof)(x) = g[f(x)] = g(|x|) = sin|x|. Now, f and g are being continuous, it follows that their composite (gof) is also continuous functions.

**NCERT Solutions for Class 12 Maths Continuity and Differentiability ****Exercise**** 5.1: Ques No 34.**

Find all the points of discontinuity of f defined by f (x) = | x | – | x + 1 |.

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