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## NCERT Class 11 Maths Textbook Chapter 13 With Answer PDF Free Download

### Chapter 13: Limits and Derivatives

#### 13.1 Introduction

This chapter is an introduction to Calculus. Calculus is a branch of mathematics which mainly deals with the study of change in the value of a function as the points in the domain change.

First, we give an intuitive idea of derivatives (without actually defining them).

Then we give a naive definition of a limit and study some algebra of limits. Then we come back to a definition of derivative and study some algebra of derivatives. We also obtain derivatives of certain

standard functions.

#### 13.2 Intuitive Idea of Derivatives

Physical experiments have confirmed that the body dropped from a tall cliff covers a distance of 4.9t 2 meters in t seconds, i.e., distance s in meters covered by the body as a function of time t in seconds is given by s = 4.9t2.

The adjoining Table 13.1 gives the distance travelled in metres at various intervals of time in seconds of a body dropped from a tall cliff. The objective is to find the velocity of the body at time t = 2 seconds from this data.

One way to approach this problem is to find the average velocity for various intervals of time ending at t = 2 seconds and hope that these throw some light on the velocity at t = 2 seconds.

Average velocity between t = t 1 and t = t2 equals distance travelled between t = t1 and t = t2 seconds divided by (t 2 – t 1). Hence the average velocity in the first two seconds

Author | NCERT |

Language | English |

No. of Pages | 40 |

PDF Size | 899 KB |

Category | Mathematics |

Source/Credits | ncert.nic.in |

### NCERT Solutions Class 11 Maths Chapter 13 Limits and Derivatives

**1. Evaluate the Given limit:**

**Solution:**

Given

Substituting x = 3, we get

= 3 + 3

= 6

**2. Evaluate the Given limit:**

**Solution:**

Given limit:

Substituting x = π, we get

= (π – 22 / 7)

**3. Evaluate the Given limit:**

**Solution:**

Given limit**:**

Substituting r = 1, we get

**= **π(1)^{2}

= π

**4. Evaluate the Given limit:**

**Solution:**

Given limit:

Substituting x = 4, we get

= [4(4) + 3] / (4 – 2)

= (16 + 3) / 2

= 19 / 2

**5. Evaluate the Given limit:**

**Solution:**

Given limit:

Substituting x = -1, we get

= [(-1)^{10} + (-1)^{5} + 1] / (-1 – 1)

= (1 – 1 + 1) / – 2

= – 1 / 2

NCERT Class 11 Maths Textbook Chapter 13 With Answer Book PDF Free Download