RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 9. Continuity

Subject: Maths - Class 12th

Q. No. 34 of Exercise 9.1

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34

If is continuous at x = 0, then find f(0).

Given:


f(x) is continuous at x = 0


If f(x) to be continuous at x = 0,then


f(0)– = f(0) + = f(0)


LHL = f(0)– =










= 1




⇒ 1


Hence,f(0) = 1


Chapter Exercises

Exercise 9.1
Exercise 9.2
Very short answer
MCQ

More Exercise Questions

1

Test the continuity of the following function at the origin :
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

If Find whether f(x) is continuous at x = 1.
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

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

Show that is discontinuous at x = 1.
12

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13

Find the value of ‘a’ for which the function f defined by is continuous at x = 0.
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

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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

Determine the values of a, b, c for which the function is continuous at x = 0.
27

If is continuous at x = 0, find k.
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

Extend the definition of the following by continuity at the point x = π.
34

If is continuous at x = 0, then find f(0).
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 :

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

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

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 :

at x = 5
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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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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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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