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

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
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