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