# NCERT solution class 11 chapter 13 Limits and Derivatives exercise 13.1 mathematics

## EXERCISE 13.1

#### Question 1:

Evaluate the Given limit:

#### Question 2:

Evaluate the Given limit:

#### Question 3:

Evaluate the Given limit:

#### Question 4:

Evaluate the Given limit:

#### Question 5:

Evaluate the Given limit:

#### Question 6:

Evaluate the Given limit:

Put x + 1 = y so that y → 1 as x → 0.

#### Question 7:

Evaluate the Given limit:

At x = 2, the value of the given rational function takes the form.

#### Question 8:

Evaluate the Given limit:

At x = 2, the value of the given rational function takes the form.

#### Question 9:

Evaluate the Given limit:

#### Question 10:

Evaluate the Given limit:

At z = 1, the value of the given function takes the form.

Put so that z →1 as x → 1.

#### Question 11:

Evaluate the Given limit:

#### Question 12:

Evaluate the Given limit:

At x = –2, the value of the given function takes the form.

#### Question 13:

Evaluate the Given limit:

At x = 0, the value of the given function takes the form.

#### Question 14:

Evaluate the Given limit:

At x = 0, the value of the given function takes the form.

#### Question 15:

Evaluate the Given limit:

It is seen that x → π ⇒ (π – x) → 0

#### Question 16:

Evaluate the given limit:

#### Question 17:

Evaluate the Given limit:

At x = 0, the value of the given function takes the form.

Now,

#### Question 18:

Evaluate the Given limit:

At x = 0, the value of the given function takes the form.

Now,

#### Question 19:

Evaluate the Given limit:

#### Question 20:

Evaluate the Given limit:

At x = 0, the value of the given function takes the form.

Now,

#### Question 21:

Evaluate the Given limit:

At x = 0, the value of the given function takes the form.

Now,

#### Question 22:

At, the value of the given function takes the form.

Now, put  so that.

#### Question 23:

Find f(x) andf(x), where f(x) =

The given function is

f(x) =

#### Question 24:

Find f(x), where f(x) =

The given function is

#### Question 25:

Evaluatef(x), where f(x) =

The given function is

f(x) =

#### Question 26:

Findf(x), where f(x) =

The given function is

#### Question 27:

Findf(x), where f(x) =

The given function is f(x) =.

#### Question 28:

Suppose f(x) = and iff(x) = f(1) what are possible values of and b?

The given function is

Thus, the respective possible values of a and b are 0 and 4.

#### Question 29:

Letbe fixed real numbers and define a function

What isf(x)? For some  computef(x).

The given function is.

#### Question 30:

If f(x) =.

For what value (s) of a does f(x) exists?

The given function is

When a < 0,

When a > 0

Thus,  exists for all a ≠ 0.

#### Question 31:

If the function f(x) satisfies, evaluate.

#### Question 32:

If. For what integers m and n does  and exist? 