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The Class 12 RD Sharma chapter 9 exercise 9.1 reference book is used by almost every student. Facing difficulty while solving the homework is no more the case, the RD Sharma Class 12 Exercise 9.1 has come to the rescue. The students need not search for the right answers on random books and websites.

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

- Chapter 9 - Differentiability -Ex-9.2
- Differentiability Excercise : FBQ
- Differentiability Excercise : MCQ
- Differentiability Excercise : VSA

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Differentiability Exercise 9.1 Question 1

**Hint:** The function y = f(x) is said to be differentiable in the closed interval [a, b] if R f ` (a) and L f ` (b) exist and f `(x) exist for every point of (a, b).

If the left hand limit, right hand limit and the value of the function at x = 3 exist and are equal to each other, then f is said to be continuous at x = 3.**Given: ****Solution:**

Therefore, we can write given function as,

But

Now Consider,

Since f(x) is continuous at x = 3, we have to find its differentiability using the formula,

Left Hand Derivate (LHD) =, denoted by L f `(c)

Right Hand Derivate (RHD =, denoted by R f `(c)

LHD at x = 3 RHD at x = 3

Hence, f(x) is continuous but not differentiable at x = 3

Differentiability Exercise 9.2 Question 2

As We Know

Differentiability Exercise 9.2 Question 3

As we know

Now, we have to check differentiability of given function at x = 3:

(LHD at x = 3) = (RHD at x = 3)

Hence, f(x) is differentiable at x = 3.

Differentiability Exercise 9.2 Question 4

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.

Now we have to check for continuity at x = 2.For continuity,

Now consider,

Since f(x) is continuous at x = 2, we have to find its differentiability using the formula,

LHD at x = 2 RHD at x = 2

Hence, f(x) is continuous but not differentiable at x = 2.

Differentiability Exercise 9.2 Question 5

**HInt ****: ** The function y = f(x) is said to be differentiable in the closed interval [a, b] if R f ` (a) and L f ` (b) exist and f `(x) exist for every point of (a, b).

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.**Given: ****Solution:**

The given function f(x) can be defined as:

We know that a polynomial and a constant function is continuous and differentiable everywhere. So f(x) is continuous and differentiable for x (-1, 0) and x (0, 1) and (1, 2).

Continuity at

Since, is continuous at x = 0.

Continuity at x = 1:

Since, is continuous at x = 1.

Differentiability at x = 0:

LHD at x = 0 RHD at x = 0

Hence, f(x) is continuous but not differentiable at x = 0.

Differentiability at x = 1:

LHD at x = 1 RHD at x = 1

Hence, f(x) is continuous but not differentiable at x = 1.

Differentiability Exercise 9.1 Question 7 Sub Question 2

Answer: f(x) is continuous but not differentiable at x = 0; if 0 < m < 1Hint: The function y = f(x) is said to be differentiable in the closed interval [a, b] if R f ` (a) and L f ` (b) exist and f `(x) exist for every point of (a, b).

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.

Now we have to check for continuity at x = 2.For continuity,

As we know and

Now consider,

As we know and

Since f(x) is continuous at x = 0, we have to find its differentiability using the formula,

Not defined

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

Hence, f(x) is continuous but not differentiable at x = 0.

Differentiability Exercise 9.1 Question 7 Sub Question 1

**Hint:** The function y = f(x) is said to be differentiable in the closed interval [a, b] if R f ` (a) and L f ` (b) exist and f `(x) exist for every point of (a, b).

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.**Given: ****Solution:**

Differentiability at x = 0:

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

Differentiability Exercise 9.1 Question 7 Sub Question 3

**Hint:** The function y = f(x) is said to be differentiable in the closed interval [a, b] if R f ` (a) and L f ` (b) exist and f `(x) exist for every point of (a, b).

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.**Given: ****Solution:**

As we know

Since RHL and LHL are not defined, f (x) is not continuous.

LHD and RHD does not exist .

Hence, f(x) is neither continuous nor differentiable at x = 0.

Differentiability Exercise 9.1 Question 8

Since f(x) is differentiable, so (LHD at x = 1) = (RHD at x = 1)

Since f(x) is differentiable, f(x) is continuous.

we Know that

Hence,

Differentiability Exercise 9.1 Question 9

If the left hand limit, right hand limit and the value of the function at x = 3 exist and are equal to each other, then f is said to be continuous at x = 3.

For continuity at x = 1,

Now consider,

Since f(x) is continuous at x = 1, we have to find its differentiability using the formula,

LHD at x = 1 RHD at x = 1. Hence, f(x) is continuous but not differentiable.

Differentiability Exercise 9.1 Question 10

Since f(x) is continuous, so LHS = RHS.

....(1)

Since f(x) is differentiable at x = 1, (LHD at x = 1) = (RHD at x = 1)

Substituting ‘a’ in (1),

Hence, and

Differentiability Exercise 9 .1 Question 11

Since f(x) is differentiable, so (LHD at x = 1) = (RHD at x = 1)

Since f(x) is differentiable, f(x) is continuous.

LHL = RHL

we know that

Hence, and

Class 12 chapter 9, Differentiability consists of only two exercises, ex 9.1 and ex 9.2. the first exercise, ex 9.1 consists of 13 questions. The various topics that this exercise includes are differentiability at a point, meaning and definition of differentiability at a point, valuable results on differentiability and differentiability in a set. The basics of it were already taught in the previous academic year.

Whenever the students get doubts regarding the differentiability concept, they can refer to the RD Sharma Class 12 Exercise 9.1 Chapter 9 Differentiability solution book. Therefore, they can solve their homework and assignments easily without facing any issues. The RD Sharma Class 12 solutions Chapter 9 exercise 9.1 also helps them in preparing for their exams.

The students will no longer feel hectic to find the right solutions for their homework or cross check it. The RD Sharma Class 12 Chapter 9 Exercise 9.1 will help the students in a better way.

The notable advantages that the students would benefit by using the RD Sharma Mathematics Solutions are:

All the questions will be answered in the RD Sharma solutions book, the students need not depend on other resources.

Questions for the public examinations are also picked from this book, hence, practicing with this reference material makes them exam-ready.

The students can learn certain small concepts way before their teacher teaches them.

Not even a penny is required to eb spent by the students.

They can cross their benchmark scores effortlessly when practised well with this book.

All the answers in the RD Sharma Class 12 Chapter 9 Exercise 9.1 are provided in the same order as given in the textbook.

- 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. How can the class 12 students get the authorized copy of the RD Sharma Class 12 Exercise 9.1 Solutions?

The authorized collection of the RD Sharma Class 12 Solutions Chapter 9 ex 9.1 is available at the Career 360 website for public access.

2. What is the feedback of the previous batch students who has used the RD Sharma solution books for their exam preparation?

The feedback provided by the previous batch students are positive. They admit that the RD Sharma Class 12 Solutions Chapter 9 ex 9.1 reference material play a vital role in making them score more marks.

3. Where can the students find the RD Sharma Class 12 maths Solutions Chapter 9 for free?

The only best site where the students can find the Class 12 RD Sharma Chapter 9 Exercise 9.1 for complete free of cost is the Career 360 website.

4. How many solved sums does the Class 12 RD Sharma Chapter 9 include?

The textbook consists of 13 questions in this exercise, therefore, the solutions for these questions can be found in the RD Sharma Solutions Class 12 Chapter 9 exercise 9.1 material.

5. Is it easy for the slow learners to adapt to the methods given in the RD Sharma books?

Students of all categories can adapt to the methods given in the RD Sharma books as many techniques are provided.

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