# NCERT Class 12-Mathematics: Chapter –5 Continuity and Differentiability Part 3

Get unlimited access to the best preparation resource for IMO-Level-2 Class-5: fully solved questions with step-by-step explanation- practice your way to success.

Question 4:

Show that the function defined by

is continuous at .

Left hand limit at is given by

Similarly

Thus, Hence is continuous at

Question 5:

Given .Find the points of discontinuity of the composite function .

We know that is discontinuous at

Now, for ,

which is discontinuous at .

Hence, the points of discontinuity are and .

Question 6:

Let , for all . Discuss the derivability of

We may rewrite

Now,

Now

Since the left hand derivative and right hand derivative both are equal, hence is differentiable at .

Question 7:

Differentiate

Let . Using chain rule, we have

Question 8:

Given . differentiating both sides w.r.t. , we have

Or

Therefore,

Question 9:

If , prove that