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

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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