RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 9. Continuity

Subject: Maths - Class 12th

Q. No. 10 of Exercise 9.1

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10

Discuss the continuity of the following functions at the indicated point(s).

at x = 0

In this problem we need to check continuity at x = 0

Given function is


at x = 0 …… Equation 2


∴ we need to check LHL, RHL and value of function at x = 0 (for idea and meaning of continuity refer to Q10(i) )


Clearly,


f(0) = 0 [from equation 2]


LHL = [∵ sin(–θ) = sinθ]


RHL = [ using eqn 2]


Why


Since whatever is value of h, sin(1/h) is going to range from –1 to 1


As h→ 0 i.e. h is approximately 0


∴ 0*some finite quantity is equal to 0.


Clearly, LHL = RHL = f(0)


∴ f(x) is continuous at x = 0


Chapter Exercises

Exercise 9.1
Exercise 9.2
Very short answer
MCQ

More Exercise Questions

1

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2

A function f(x) is defined as Show that f(x) is continuous at x = 3.
3

A function f(x) is defined as

Show that f(x) is continuous at x = 3.
4

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5

If Find whether f(x) is continuous at x = 0.
6

If Find whether f is continuous at x = 0.
7

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8

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9

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10

Discuss the continuity of the following functions at the indicated point(s).

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10

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10

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10

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10

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10

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10

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11

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12

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13

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14

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15

Discuss the continuity of the function at the point x = 0.
16

Discuss the continuity of the function at the point x = 1/2.
17

Discuss the continuity of at x = 0.
18

For what value of k is the function continuous at
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19

Determine the value of the constant k so that the function is continuous at x = 1.
20

For what value of k is the function continuous at
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21

Determine the value of the constant k so that the function is continuous at x = 2.
22

Determine the value of the constant k so that the function is continuous at x = 0.
23

Find the values of a so that the function is continuous at x = 2.
24

Prove that the function remains discontinuous at x = 0, regardless of the choice of k.
25

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26

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27

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28

If is continuous at x = 4, find a, b.
29

For what value of k is the function continuous at x = 0?
30

Let x ≠ 0. Find the value of f at x = 0 so that f becomes continuous at x = 0.
31

If is continuous at x = 2, find k.
32

If is continuous at x = 0, find k.
33

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34

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35

Find the value of k for which is continuous at x = 0.
36

In each of the following, find the value of the constant k so that the given function is continuous at the indicated point :

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36

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36

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36

In each of the following, find the value of the constant k so that the given function is continuous at the indicated point :

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36

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36

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37

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38

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39

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39

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40

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41

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42

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43

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44

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45

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