NCERT Solutions for Class 12-science Maths Chapter 5 - Continuity and Differentiability

Your CBSE Class 12 syllabus for Maths consists of topics such as linear programming, vector quantities, determinants, etc. which lay the foundation for further education in science, engineering, management, etc. Studying differential equations will be useful for exploring subjects such as Physics, Biology, Chemistry, etc. where your knowledge can be applied for scientific investigations.

On TopperLearning, you can find study resources such as sample papers, mock tests, Class 12 Maths NCERT solutions and more. These learning materials can help you understand concepts such as differentiation of functions, direction cosines, integrals, and more. Also, you can practise the Maths problems by going through the solutions given by our experts.

Maths is considered as one of the most difficult subjects in CBSE Class 12 Science. Our Maths experts simplify complex Maths problems by assisting you with the right methods to solve problems and score full marks. You may still have doubts while referring to the Maths revision notes or Maths NCERT solutions. Solve those doubts by asking an expert through the “Undoubt” feature on the student dashboard.

Read  more

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.1

Solution 1

The given function is f(x) = 5x - 3

At x = 0, f(0) = 5 × 0 - 3 = -3

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 2

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 3

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 4

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 5

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 6

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 7

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 8

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 9

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 10

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 11

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 12

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
 
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Thus, from the above observation, it can be concluded that x = 1 is the only point of discontinuity.
 
Solution 13

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 14

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 15

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 16

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 17

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 18

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 19

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 20

The given function is f(x) = x2 - sinx + 5

It is evident that f is defined at x = ∏

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 21

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 22

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Therefore, cosecant is continuous except at x = np, n Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And DifferentiabilityZ
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Therefore, cotangent is continuous except at x = np, n Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And DifferentiabilityZ
Solution 23

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 24

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

 
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 25

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 26

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 27

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 28

 

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

The given function f is continuous at x = Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability, if f is defined at x = Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability and if the value

of f at x = Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability equals the limit of f at x = Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 29

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 30

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 31

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 32

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 33

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
 
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 34

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.2

Solution 1

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Then, (v ο u)(x) = v(u(x)) = v(x2 + 5) = sin (x2 + 5) = f(x)

 

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 2

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 3

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 4

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 5

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 6

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 7

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 8

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 9

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 10

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.3

Solution 1

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 2

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 3

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 4

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 5

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 6

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 7

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 8

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 9

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 10

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 11

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 12

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 13

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 14

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 15

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.4

Solution 1

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 2

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 3

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 4

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 5

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 6

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 7

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 8

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 9

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 10

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.5

Solution 1

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 2

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 3

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 4

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 5

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 6

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 7

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 8

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 9

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 10

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 11

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 12

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 13

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 14

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 15

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 16

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 17

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 18

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.6

Solution 1

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 2

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 3

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 4

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 5

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 6

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 7

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 8

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 9

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 10

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 11

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.7

Solution 1

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 2

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 3

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 4

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 5

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 6

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 7

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 8

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 9

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 10

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 11

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 12

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 13

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 14

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 15

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 16

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 17

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.8

Solution 1

 

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Rolle's theorem states that there is a point c Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability (-4, -2) such that f'(c) = 0

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 2

 

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

then there exists some c Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability(a, b) such that f'(c) = 0

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Let n be an integer such that n Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability (5, 9).

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Let n be an integer such that n Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability (-2, 2).

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 3

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Therefore, by the Mean Value Theorem, there exists c Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability (-5, 5) such that

 

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 4

 

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Mean Value Theorem states that there is a point c Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability(1, 4) such that f'(c) = 1

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 5

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 6

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Chapter 5 - Continuity and Differentiability Exercise Misc. Ex.

Solution 1

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 2

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 3

 Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 4

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 5

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 6

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 7

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 8

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 9

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

 

where sin x > cosx 

Solution 10

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 11

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 12

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 13

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 14

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 15

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
 
Hence, proved.
Solution 16

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

 

Solution 17

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 18

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 19

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Solution 20

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 21

 Yes.

Consider the function f(x)=|x-1|+|x-2|

Since we know that the modulus function is continuous everywhere, so there sum is also continuous

Therefore, function f is continuous everywhere

Now, let us check the differentiability of f(x) at x=1,2

At x=1

LHD = Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

 [Take x=1-h, h>0 such that h0 as x1-]

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability 

Now,

RHD = Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

 [Take x=1+h, h>0 such that h0 as x1+]

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

≠ LHD

Therefore, f is not differentiable at x=1.

 

At x=2

LHD = Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

 [Take x=2-h, h>0 such that h0 as x2-]

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability 

Now,

RHD = Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

 [Take x=2+h, h>0 such that h0 as x2+]

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

≠ LHD

Therefore, f is not differentiable at x=2.

Hence, f is not differentiable at exactly two points.

Solution 22

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Solution 23

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability

Ncert Solutions Cbse Class 12-science Mathematics Chapter - Continuity And Differentiability
Loading...

Why CBSE Class 12 Science Maths solutions are important?

Maths is a subject which requires practising a variety of problems to understand concepts clearly. By solving as many problems as you can, you’ll be able to train your brain in thinking the logical way to solve maths problems. For practising problems, study materials such as sample papers, previous year papers, and NCERT solutions are needed.

Some of the best Maths experts work with us to give you the best solutions for Maths textbook questions and sample paper questions. Chapter-wise NCERT solutions for Class 12 Science Maths can be easily accessible on TopperLearning. Use these solutions to practise problems based on concepts such as direction ratios, probability, area between lines, inverse trigonometric functions, and more.

To prepare for your Maths exam, you need to attempt solving different kinds of Maths questions. One of the best ways to assess your problem-solving abilities is to attempt solving previous year papers with a set timer. Our Maths solutions will come in handy to help you with checking your answers and thus, improving your learning experience. So, to score more marks in your Class 12 board exams, use our Maths solutions that will enable you with the appropriate preparation.