NCERT Solutions for Class 11 Maths Chapter 13 – Limits and Derivatives Ex 13.1

NCERT Solutions for Class 11 Maths Chapter 13 – Limits and Derivatives Ex 13.1

Page No 301:

Question 1:

Evaluate the Given limit:

Answer:

Question 2:

Evaluate the Given limit:

Answer:

Question 3:

Evaluate the Given limit:

Answer:

Question 4:

Evaluate the Given limit:

Answer:

Question 5:

Evaluate the Given limit:

Answer:

Question 6:

Evaluate the Given limit:

Answer:

Put x + 1 = y so that y → 1 as x → 0.

Question 7:

Evaluate the Given limit:

Answer:

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

Question 8:

Evaluate the Given limit:

Answer:

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

Question 9:

Evaluate the Given limit:

Answer:

Question 10:

Evaluate the Given limit: 

Answer:

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:

Answer:

Question 12:

Evaluate the Given limit:

Answer:

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

Question 13:

Evaluate the Given limit:

Answer:

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

Question 14:

Evaluate the Given limit:

Answer:

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

Page No 302:

Question 15:

Evaluate the Given limit:

Answer:

It is seen that x → π ⇒ (π – x) → 0

Question 16:

Evaluate the given limit: 

Answer:

Question 17:

Evaluate the Given limit:

Answer:

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

Now,

Question 18:

Evaluate the Given limit:

Answer:

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

Now,

Question 19:

Evaluate the Given limit:

Answer:

Question 20:

Evaluate the Given limit:

Answer:

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

Now,

Question 21:

Evaluate the Given limit:

Answer:

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

Now,

Question 22:

Answer:

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

Now, put  so that.

Question 23:

Find f(x) andf(x), where f(x) =

Answer:

The given function is

f(x) =

Question 24:

Find f(x), where f(x) =

Answer:

The given function is

Question 25:

Evaluatef(x), where f(x) = 

Answer:

The given function is

f(x) = 

Question 26:

Findf(x), where f(x) =

Answer:

The given function is

Question 27:

Findf(x), where f(x) =

Answer:

The given function is f(x) =.

Question 28:

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

Answer:

The given function is

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

Page No 303:

Question 29:

Letbe fixed real numbers and define a function

What isf(x)? For some  computef(x).

Answer:

The given function is_.

Question 30:

If f(x) =.

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

Answer:

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.

Answer:

Question 32:

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

Answer:

The given function is

Thus,  exists if m = n.

Thus, exists for any integral value of m and n.