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: