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Edited By Kuldeep Maurya | Updated on Jan 20, 2022 04:11 PM IST

Class 12 RD Sharma chapter 9 exercise 9.2 solution book is now available for the welfare of the class 12 students. The expert provided solution book is a boon for the class 12 students to learn mathematical concepts easily. Therefore, the RD Sharma Class 12 Solutions Differentiability Ex 9.2 serves an essential purpose for the students.

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**Also Read - **RD Sharma Solution for Class 9 to 12 Maths

- Chapter 9 - Differentiability -Ex-9.1
- Differentiability Excercise : FBQ
- Differentiability Excercise : MCQ
- Differentiability Excercise : VSA

Differentiability Excercise:9.2

Differentiability Exercise 9.2 Question 1

Differentiating f(x) w.r.t x then,

Now put x = 2 in f `(x), then

Differentiability Exercise 9.2 Question 3

Differentiating f(x) w.r.t x then,

Now,

[Equal]

Differentiability Exercise 9.2 Question 4

Differentiating f(x) w.r.t x then,

We Know that

Differentiability Exercise 9.2 Question 5

Differentiating f(x) w.r.t x then,

Now, for f ` (4), we will put x = 4 in f ` (x), then:

Differentiability Exercise 9.2 Question 6

Differentiating f(x) w.r.t x then,

f `(x) = m

For f `(0), put x = 0 in f `(x), then

f `(x) = m

f ` (x) is not affected at x = 0, since in f `(x) there is no term of x.

Differentiability Exercise 9.2 Question 7

To check differentiability at x = -2,

(LHD at x = -2) (RHD at x = -2)

Thus, f(x) is not differentiable at x = -2.

Now, we need to check differentiability at x = 0.

(LHD at x = 0) = (RHD at x = 0)

Thus, f(x) is differentiable at x = 0.

Differentiability Exercise 9.2 Question 8

We know that, polynomial functions are always continuous and differentiable.

Let us consider,

Modulus functions are always continuous.

So, is continuous.

Now, there is more than one slope possible. So it is not differentiable as we know that

Using mod function, we can write the function which is non-derivable at exactly 5 points and continuous always is

Differentiability Exercise 9.2 Question 9

The given function is absolute function. So it is continuous. Consider the graph of the given function.

Using graphs of the function, we can observe that the function f(x) is not differentiable at x= --1 and x = 1 but continuous for all x expect 0

Differentiability Exercise 9.2 Question 10

We know that exponential function is always continuous. So, the given function is continuous. Consider the graph of the given function.

Using graph of the function, it is clear that f(x) is not differentiable at x = 0 but continuous for all x.

Differentiability Exercise 9.2 Question 11

It is given that, f(c) = 0.

Consider,

Substituting x – c = y, we get:

So,

Thus, f(x) is continuous at x = c.

Now, we need to check differentiability at x=c.

Using the formula, we have:

So, LHD is given by,

Put x = c – h

Since the value of cos is going to infinity, its limit will oscillate between -1 and 1.

Now, R.H.D is given by,

Since the value of cos is going to infinity, its limit will oscillate between -1 and 1. As the value of limit is not a finite value, the function is not differentiable.

Differentiability Exercise 9.2 Question 12

Check LHD at is equal to RHD at or not for is even and is odd respect for the function

Given functions are and .

Let

Case 1

For (Where is even)

LHD at

LHD at … (i)

RHD at

RHD at ....(iii)

From(i) and (ii)

LHD at

Case II

For (Where is odd)

LHD at

RHD at .....(iv)

From (iii) and (iv)

LHD at

Thus, is not differentiable at

Now we need to check is differentiable or not

Let,

is differentiable everywhere.

Differentiability Exercise 9.2 Question 6

If the left hand limit, right hand limit and the value of the function at x = c exist and are equal to each other, then f is said to be continuous at x = c.

Differentiability at x = 1:

(LHD at x = 0)= (RHD at x = 0)

Hence, f(x) is differentiable at x = 0.

The chapter 9 in mathematics for class 12 consists of two exercises, ex 9.1 and 9.2. the second or the last exercise, ex 9.2 consists of 12 questions to be solved. It covers the topics like differentiability at a point, derivative of the capacity and differentiability in a set. All the solutions for these questions can be found at the RD Sharma Class 12 Solutions Chapter 9 exercise 9.2 reference book.

The Class 12 RD Sharma chapter 9 exercise 9.2 reference material contains additional questions and sample question papers. This allows the students to try various mock tests before facing a class test or exam. Therefore, RD Sharma Class 12 Solutions Chapter 9 Exercise 9.2 makes the students exam-ready.

Continuous practice with the RD Sharma Class 12th Exercise 9.2 Chapter 9 Differentiability solution book will increase their speed in finding the answers. As a result, they would have a lot of time to recheck their answers after writing the exam.

Here are some of the benefits that the students who use the RD Sharma solution books would reap:

The solution books are available at the Career 360 website where not even a single rupee is required to be paid.

The RD Sharma Class 12 Solutions Chapter 9 ex 9.2 can be downloaded as a PDF file at an instance.

Formulae are provided separately for convenience.

The sums are solved in many methods.

Students cross their benchmark scores effortlessly due to proper practice.

All the sums are solved in the same order as present in the textbook to avoid confusion.

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

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Download E-book1. What is the proper way to attain the RD Sharma Class 12th exercise 9.2 Solutions on the Career 360 website?

Not every website provides the authorized set of books, therefore, download the RD Sharma Class 12th Chapter 9 Exercise 9.2 material from the Career 360 website.

2. How many questions are asked in ex 9.2 of class 12 mathematics?

This exercise consists of 12 questions that are solved in the RD Sharma Class 12 Chapter 9 Exercise 9.2 book.

3. Can everyone utilize the RD Sharma Class 12 Mathematics chapter 9 solutions book?

Yes, there are no restrictions or specific access given in use the RD Sharma books in the career 360 website. Therefore, everyone can access it easily.

4. What makes the Class 12 RD Sharma Chapter 9 Exercise 9.2 solution book the best option to select?

Some of the questions for the public exams in the previous years were asked from the Class 12 RD Sharma Chapter 9 exercise 9.2 book. therefore, it is a wise man’s option to select this book.

5. Are the solutions provided in the RD Sharma solutions accurate?

Distinct experts have contributed their knowledge and skill in developing this set of solution books. Therefore, the students are assured about the accuracy of the solutions.

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