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Class 12-science RD SHARMA Solutions Maths Chapter 9 - Continuity

Continuity Exercise Ex. 9.1

Solution 42

Given:

At x = 0, we have

LHL RHL

So, f(x) is discontinuous at x = 0.

Thus, there is no value of  for which f(x) is continuous at x = 0.

At x = 1, we have

LHL = RHL

So, f(x) is continuous at x = 1.

At x = -1, we have

LHL = RHL

So, f(x) is continuous at x = -1.

Continuity Exercise MCQ

Solution 1

Correct option: (c)

Solution 2

Correct option: (a), (b)

Solution 3

Correct option: (a),(d)

Solution 4

Correct option: (c)

Solution 5

Correct option: (d)

Solution 6

Correct option: (c)

Solution 7

Correct option: (c)

Solution 8

Correct option: (b)

Solution 9

Correct option: (b)

Solution 10

Correct option: (d)

Solution 11

Correct option: (b)

Solution 12

Correct option: (a)

Solution 13

Correct option: (d)

Solution 14

Correct option: (c)

Solution 15

Correct option: (c)

Solution 16

Correct option: (c)

Solution 17

Correct option: (c)

Solution 18

Correct option: (c)

Solution 19

Correct option: (d)

Solution 20

Correct option: (b)

Solution 21

Correct option: (a)

Solution 22

Correct option: (a)

Solution 23

Correct option:(d)

Solution 24

Correct option: (c)

Solution 25

Correct option: (b)

Solution 26

Correct option: (b)

Solution 27

Correct option: (a)

Solution 28

Correct option: (a)

Solution 29

Correct option: (b)

Solution 30

Correct option: (a)

Solution 31

Correct option: (a)

Solution 32

Correct option: (d)

Solution 33

Correct option: (b)

Solution 34

Correct option: (b)

Solution 35

Correct option: (a)

Solution 36

Correct option: (d)

Solution 37

Correct option: (c)

Solution 38

Correct option: (b)

Solution 39

Correct option: (b)

Solution 40

Correct option: (b)

Solution 41

Correct option: (d)

Solution 42

Correct option: (a)

Solution 43

We know that, if f(x) and g(x) are continuous then

[f(x) + g(x)], [f(x) - g(x)], f(x)g(x) are continuous functions.

Now,

For f(x) = 0

4x = 0

x = 0

Thus,  is discontinuous at x =0.

Solution 44

The function f(x) = cot x is discontinuous if cot x

Solution 45

Given:

As f(x) is continuous at x = 0, then

Hence, the value of f(x) is 0.

Solution 46

Given:

As {x} = 0 for integral values of x.

Therefore, domain of f(x) is set of all non-integral values.

Thus, f(x) is discontinuous at all integers.

Solution 47

The function f(x) = [x] is continuous everywhere except for integral values.

Therefore, f(x) = [x] is continuous at x = 1.5.

Solution 48

Given:

As f(x) is continuous at x = 0, we have

Continuity Exercise Ex. 9VSAQ

Solution 11

Given:

As f(x) is continuous at x = 0, we have

Solution 12

Given:

As f(x) is continuous at x = 2, we have