Solution of Chapter 13. limits and derivatives (NCERT - Maths Book)

Chapter Exercises

Exercise 13.1
Exercise 13.2
Miscellaneous Exercise

Exercise 13.1

1

Evaluate the following limits in Exercises.
2

Evaluate the following limits in Exercises.
3

Evaluate the following limits in Exercises.
4

Evaluate the following limits in Exercises.
5

Evaluate the following limits in Exercises.
6

Evaluate the following limits in Exercises.
7

Evaluate the following limits in Exercises.
8

Evaluate the following limits in Exercises.
9

Evaluate the following limits in Exercises.
10

Evaluate the following limits in Exercises.
11

Evaluate the following limits in Exercises.
12

Evaluate the following limits in Exercises.
13

Evaluate the following limits in Exercises.
14

Evaluate the following limits in Exercises.
15

Evaluate the following limits in Exercises.
16

Evaluate the following limits in Exercises.
17

Evaluate the following limits in Exercises.
18

Evaluate the following limits in Exercises.
19

Evaluate the following limits in Exercises.
20

Evaluate the following limits in Exercises.
21

Evaluate the following limits in Exercises.
22

Evaluate the following limits in Exercises.
23

Find and , where

24

Find , where
25

Evaluate , where f(x) =
26

Find, where
27

Find , where

28

Suppose

and if = f (1) what are possible values of a and b?
29

Let a1, a2,… , an be fixed real numbers and define a function

f (x) = ( x − a1) ( x − a2)...( x − an) .


What is ? For some compute .
30

If For what value (s) of a does exists?
31

If the function f(x) satisfies , evaluate
32

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

Exercise 13.2

1

Find the derivative of x2 – 2 at x = 10.
2

Find the derivative of 99x at x = l00.
3

Find the derivative of x at x = 1.
4

Find the derivative of the following functions from first principle.

x3 – 27
4

Find the derivative of the following functions from first principle.

(x −1) (x − 2)
4

Find the derivative of the following functions from first principle.
4

Find the derivative of the following functions from first principle.
5

For the function .Prove that f’ (1) =100 f’ (0).
6

Find the derivative of for some fixed real number a.
7

For some constants a and b, find the derivative of

(x − a) (x − b)
7

For some constants a and b, find the derivative of
7

For some constants a and b, find the derivative of
8

Find the derivative of for some constant a.
9

Find the derivative of
9

Find the derivative of
9

Find the derivative of
9

Find the derivative of
9

Find the derivative of
9

Find the derivative of
10

Find the derivative of cos x from first principle.
11

Find the derivative of the following functions:

sin x cos x
11

Find the derivative of the following functions:

sec x
11

Find the derivative of the following functions:

5sec x + 4cos x
11

Find the derivative of the following functions:

cosec x
11

Find the derivative of the following functions:

3 cot x + 5 cosec x
11

Find the derivative of the following functions:

5 sin x – 6 cos x + 7
11

Find the derivative of the following functions:

2tan x – 7sec x

Miscellaneous Exercise

1

Find the derivative of the following functions from first principle:

–x
1

Find the derivative of the following functions from first principle:

(-x)-1
1

Find the derivative of the following functions from first principle:

sin (x + 1)
1

Find the derivative of the following functions from first principle:
2

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (x + a)
3

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
4

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
5

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
6

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
7

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
8

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
9

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
10

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
11

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
12

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

(ax + b)n
13

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
14

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

sin (x+a)
15

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

cosec x cot x
16

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
17

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
18

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
19

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

20

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
21

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
22

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
23

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
24

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
25

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
26

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
27

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
28

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
29

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
30

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):