RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 9. Continuity and Differentiability

Subject: Maths - Class 12th

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Chapter Exercises

Exercise 9A
Exercise 9B
Exercise 9C

Exercise 9A

1

Show that ƒ(x) = x2 is continues at x=2.
2

Show that ƒ(x) = (x2+3x+4) is continuous at x=1.
3

Prove that

ƒ(x) =is continuous at x=3
4

Prove that

ƒ(x) = is continuous at x=5
5

Prove that

ƒ(x) = is discontinuous at x=0
6

Prove that

ƒ(x) =is discontinuous at x=0
7

Prove that

ƒ(x) =is discontinuous at x=2
8

Prove that

ƒ(x) =is discontinuous at x=0
9

Prove that

ƒ(x) = is continuous at x=1
10

Prove that

ƒ(x) = is continuous at x=2
11

Prove that

ƒ(x) =is discontinuous at x=0
12

Prove that

ƒ(x) =is discontinuous at x=a
13

Prove that

ƒ(x) =is discontinuous at x=0
14

Prove that

ƒ(x) =is discontinuous at x=0
15

Prove that

ƒ(x) = is discontinuous at x=2
16

Prove that

ƒ(x) =is discontinuous at x=0
17

Find the value of k for which

ƒ(x) = is continuous at x=0
18

Find the value of λ for which

ƒ(x) = is continuous at x=-1
19

For what valve of k is the following function continuous at x=2

ƒ(x) =


20

For what valve of k is the following function

ƒ(x) = is continuous at x=3


Ans. k=6
21

For what valve of k is the following function

ƒ(x) = is continuous at x=


Ans. k=6
22

Show that function:

ƒ(x) = is continuous at x=0
23

Show that: ƒ(x) = is continuous at x=1
24

Show that: ƒ(x) = is continuous at x=2
25

Find the values of a and b such that the following functions continuous.
26

Find the values of a and b such that the following functions ƒ, defined asis continuous at x=0
27

Prove that the function ƒ given ƒ(x)=|x-3|, x є R is continuous but not differentiable at x=3

Exercise 9B

1

Show that function ƒ(x) = is continuous function.
2

Show that function ƒ(x) = is continuous.
3

Show that function ƒ(x) = is continuous.
4

Show that sec x is a continuous function.
5

Show that sec |x| is a continuous function
6

Show that function ƒ(x) = is continuous.
7

Discuss the continuity of f(x) = [x].
8

Show that ƒ(x) = is continuous.
9

Show that ƒ(x) = is continuous at each point except 0.
10

Locate the point of discontinuity of the function

ƒ(x) =


11

Discus the continuity of the function ƒ(x)= |x|+|x-1| in the interval of [-1, 2]

Exercise 9C

1

Show that ƒ(x) = x3 is continuous as well as differentiable at x=3.
2

Show that ƒ(x) = (x-1)1/3 is not differentiable at x=1.
3

Show that constant function is always differentiable
4

Show that ƒ(x) = |x-5| is continuous but not differentiable at x=5
5

Let ƒ(x) =

Show that ƒ(x) is continuous but not differentiable at x=1
6

Show that ƒ(x) = [x] is neither continuous nor derivable at x=2.
7

Show that function

ƒ(x) = is continuous but not differentiable at x=1
8

Let ƒ(x) = Show that ƒ(x) is not derivable at x=0.
9

If ƒ(x) = |x| show that ƒ’(2)=1
10

Find the values of a and b so that the function

ƒ(x) = is differentiable at each x є R