# CBSE Class 12 Mathematics NCERT Exemplar Solutions: Chapter- Continuity and Differentiability

Jul 20, 2018 17:34 IST
Class 12 Mathematics NCERT Exemplar Solutions: Continuity and Differentiability

The NCERT Exemplar books are very important for engineering entrance exams like JEE Main, WBJEE and UPSEE as the level of the questions are very high. The questions given at the end of the chapter are very important for board exams also. Sometimes, students got confused while solving the questions given in NCERT Exemplar books. In this article, we providing you NCERT Exemplar Solutions Class 12 Mathematics Chapter 5 – Continuity and Differentiability Students can take help from these solutions if they stuck while solving any question. The solutions are presented in the most appropriate and simple way for easy understanding.

## What topics will you read in chapter - Continuity and Differentiability?

 Concept of continuity and differentiability Derivative of Composite functions Differentiation of Inverse trigonometric functions Derivative of Implicit functions Concept of exponential & logarithmic functions Derivative of functions expressed in parametric forms Second order derivatives Rolle's Theorem Lagrange's Mean Value Theorem

## Few problems along with their solutions from this chapter are given follows:

Question:

Examine the continuity of the function f (x) = x3 + 2x2 - 1 at x = 1.

Solution:

Question:

An example of a function which is continuous everywhere but fails to be differentiable exactly at two points is ........  .

Solution:

An example of a function which is continuous everywhere but fails to be differentiable exactly at two points is x + |x – 1|. The functions is continuous everywhere but fails to be differentiable exactly at two points x = 0 and x = 1.

Question:

If f is continuous on its domain D, then | f | is also continuous on D.

Solution: True

If a function is continuous on its domain, then the modulus of the function is also continuous in the same domain.

Hence, | f |is also continuous on D.

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Question:

The composition of two continuous functions is a continuous function.

Solution: True

The composition of two continuous functions is also a continuous function

Question:

Trigonometric and inverse trigonometric functions are differentiable in their respective domain.

Solution: True

All the trigonometric and inverse trigonometric functions are differentiable in their respective domain.

## Why students should read Class 12 NCERT Exemplar Books?

• Offers in-depth knowledge of each topic.
• Strictly follows the CBSE board curriculum.
• Questions are frequently asked in board exams.
• Important questions are given at the end of each chapter
• NCERT Exemplar books are written in an easy language by experienced teachers and professor having deep understanding of the subject.
• NCERT Exemplar books help students to understand the basics and fundamentals
• Contain standard questions plus some extra information for competitive exams.
• Many questions are asked in engineering entrance exams like JEE-Main from NCERT Exemplar books.

## In this chapter of the book, students will get the following things.

 Brief summary of the complete chapter Short answer type questions Long answer types questions Objective type questions or MCQs Fill in the blanks True and False

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