# NCERT Class 12-Mathematics: Chapter – 5 Continuity and Differentiability Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 4**:

Show that the function defined by

is continuous at .

**Answer**:

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 .

**Answer**:

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

**Answer**:

We may rewrite

Now,

Now

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

**Question 7**:

Differentiate

**Answer**:

Let . Using chain rule, we have

**Question 8**:

**Answer**:

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

Or

Therefore,

**Question 9**:

If , prove that

**Answer**:

Given that . Differentiating both sides , we have

Or

Which implies that