RD Sharma Solutions For Class 12 Maths Exercise 9.1

This exercise has problems which are solved on continuity of function by the subject experts at BYJU’S. Our team of faculty mainly work with the aim of making Mathematics easier for students based on their grasping power. The students can gain a grip on the concepts covered in Maths Class 12 only by regular practise, and while solving can make use of the PDF as a reference. Students can easily download the RD Sharma Solutions for Class 12 Maths Exercise 9.1 of Chapter 9 from the below provided links.

Let us have a look at some of the topics that are discussed in this exercise.

  • The intuitive notion of continuity
  • Continuity at a point
  • Algebra of continuous function
    • Testing the continuity of a function at a point when the function has the same definition on both sides of the given point
    • Testing continuity of a function at a point when the function has different definitions on both sides of the given point
    • Finding the values of a constant given in the definition of a function when it is continuous at an indicated point
    • On continuity of composite function

RD Sharma Solutions For Class 12 Chapter 9 – Continuity Exercise 9.1:-Download PDF Here

RD Sharma Class 12 Maths Solutions Chapter 9 Continuity Exercise 9.1
RD Sharma Class 12 Maths Solutions Chapter 9 Continuity Exercise 9.1 1
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Access another exercise of RD Sharma Solutions For Class 12 Chapter 9 – Continuity

Exercise 9.2 Solutions

Access answers to Maths RD Sharma Solutions For Class 12 Chapter 9 – Continuity Exercise 9.1

Exercise 9.1 Page No: 9.16

1. Test the continuity of the following function at the origin:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 1

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 2

Consider LHL at x = 0

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 3

2. A function f(x) is defined as

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 4

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

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 5

3. A function f(x) is defined as

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 6

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

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 7
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 8

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 9

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

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 10
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 11
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 12

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

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 13
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 14
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 15

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

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 16
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 17
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 18
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 19

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 20
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 21
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 22
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 23

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 24
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 25
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 26

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 27
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 28

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

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 29

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 30
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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 33
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Solution:

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 38
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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 41
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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 44
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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 47
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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 50
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Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 52
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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 54
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13. Find the value of a for which the function f defined by

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 57

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 58
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 59
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 60

14. Examine the continuity of the function

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 61

Also sketch the graph of this function.

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 62
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 63

Hence f (x) is discontinuous at x = 0

15. Discuss the continuity of the function

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 64

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 65

16. Discuss the continuity of the function

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 66

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 67
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 68

17. Discuss the continuity of

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 69

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 70
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 71

18. For what value of k is the function

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 72

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 73

19. Determine the value of the constant k so that the function

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 74

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 75

20. For what value of k is the function

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 76

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 77
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 78

21. Determine the value of the constant k so that the function

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 79

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 80
RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 81

22. Determine the value of the constant k so that the function

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 82

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 83

23. Find the values of a so that the function

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 84

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 9 Continuity Image 85

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