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# NCERT Solutions - Continuity & Differentiability, Exercise 5.2 JEE Notes | EduRev

## JEE : NCERT Solutions - Continuity & Differentiability, Exercise 5.2 JEE Notes | EduRev

The document NCERT Solutions - Continuity & Differentiability, Exercise 5.2 JEE Notes | EduRev is a part of the JEE Course Mathematics (Maths) Class 12.
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Continuity & Differentiability

Question 1: Differentiate the functions with respect to x.

Question 2: Differentiate the functions with respect to x. cos(sinx)

Thus, f is a composite function of two functions.

Put t = u (x) = sin x

By chain rule,
Alternate method

Question 3: Differentiate the functions with respect to x.

sin(ax + b)

Alternate method

Question 4: Differentiate the functions with respect to x.

Hence, by chain rule, we obtain

Question 5: Differentiate the functions with respect to x.

The given function is

Put y = p (x) = cx + d

Question 6: Differentiate the functions with respect to x.

Question 7:  Differentiate the functions with respect to x.

Question 8: Differentiate the functions with respect to x.

Clearly, f is a composite function of two functions, u and v, such that

Alternate method

Question 9:
Prove that the function f given by  is not differentiable at x = 1.

The given function is

It is known that a function f is differentiable at a point x = c in its domain if both

are finite and equal.

To check the differentiability of the given function at x = 1,

consider the left hand limit of f at x = 1

Since the left and right hand limits of f at x = 1 are not equal, f is not differentiable at x = 1

Question 10:
Prove that the greatest integer function   defined by is not differentiable at x = 1 and x = 2.

The given function f is
It is known that a function f is differentiable at a point x = c in its domain if both

are finite and equal.

To check the differentiability of the given function at x = 1, consider the left hand limit  of f at x = 1

Since the left and right hand limits of f at x = 1 are not equal, f is not differentiable at x = 1

To check the differentiability of the given function at x = 2, consider the left hand limit of f at x = 2

Since the left and right hand limits of f at x = 2 are not equal, f is not differentiable at x = 2

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## Mathematics (Maths) Class 12

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