# NCERT Class 12-Mathematics: Chapter – 5 Continuity and Differentiability Part 13 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 23**:

Show that is continuous but not differentiable at .

**Answer**:

We have

For continuity at ,

Hence, is continuous at .

Now,

So, is not differentiable at .

**Question 24**:

A function satisfies the equation for all , . Suppose that the function is differentiable at and . Prove that .

Differentiate each of the following w. r. t. (Exercises 25 to 43) :

**Answer**:

Let satisfies the equation

Let is differentiable at and

Also,

**Question 25**:

Differentiate each of the following w. r. t.

**Answer**:

**Question 26**:

Differentiate each of the following w. r. t. x

**Answer**:

**Question 27**:

**Answer**:

**Question 28**:

**Answer**:

**Question 29**:

**Answer**:

**Question 30**:

**Answer**:

**Question 31**:

**Answer**: