NCERT Class 12-Mathematics: Chapter – 5 Continuity and Differentiability Part 6 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 21:

For what value of is continuous at ?

Answer:

Here Left hand limit of at is

And right hand limit of at is

Thus . Hence is continuous at only if

Question 22:

Examine the differentiability of the function defined by

Answer:

The only doubtful points for differentiability of are and . Differentiability at .

Now

Thus . Therefore f is not differentiable at . Similarly, for differentiability at , we have

Which does not exist. Hence is nor differentiable at

Question 23:

Differentiate with respect to where .

Answer:

Let .

We want to find

Now

Then

Hence

Now