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

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**Question 15**:

Prove that the function defined by

Remains discontinuous at x = 0, regardless the choice of k.

**Answer**:

At

And

Since, for any value of

Hence, is discontinuous at regardless the choice of

**Question 16**:

Find the values of and such that the function defined by

Is a continuous function at .

**Answer**:

**Question 17**:

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

**Answer**:

Discontinuous at

**Question 18**:

Find all points of discontinuity of the function , where

**Answer**:

Discontinuous at and ,

**Question 19**:

Show that the function is continuous at . Examine the differentiability of , where is defined by

**Answer**:

We have

Let

And

Since, is a continuous function as it is forming with addition of two continuous function and .

Also, is also a continuous function.

Hence, is a continuous function everywhere.

So, is continuous at

**Question 20**:

**Answer**:

Not differentiable at

**Question 21**:

**Answer**:

Differentiable at

**Question 22**:

**Answer**:

Not differentiable at