# NCERT Class 11-Math՚S: Chapter – 13 Limits and Derivatives Part 10 (For CBSE, ICSE, IAS, NET, NRA 2022)

Get top class preparation for IMO right from your home: fully solved questions with step-by-step explanation- practice your way to success.

**Question 45**:

**Answer**:

Let

Subtracting eq. (i) from eq. (ii) ,

Dividing both sides by ∆ x and taking the limit,

By differentiation,

Expanding by binomial theorem, and rejecting the higher powers of

Hence, the answer is

**Question 46**:

**Answer**:

Let

Subtracting eq. (i) from eq. (ii) ,

Dividing both sides by ∆ x and take the limits,

Taking the limits,

Hence the answer is

## Evaluate Each of the Following Limits in Exercises 47 to 53

**Question 47**:

**Answer**:

**Question 48**:

**Answer**:

**Question 49**:

**Answer**:

**Question 50**:

**Answer**: