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RD Sharma Solution for Class 12 Science Mathematics Chapter 9 - Continuity

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Our RD Sharma Textbook Solutions are considered extremely helpful for solving the tough questions which are asked in the CBSE Class 12 exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 9 - Continuity.

All our solutions are created in accordance with the latest CBSE syllabus, and they are amended from time to time to provide the most relevant answers. Our free RD Sharma Solutions for CBSE Class 12 Mathematics will strengthen your fundamentals in Mathematics and will help you in your attempts to score more marks in the final examination. CBSE Class 12 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

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Exercise/Page

RD Sharma Solution for Class 12 Science Mathematics Chapter 9 - Continuity Page/Excercise 9.1

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10(i)


Solution 10(ii)

Solution 10(iii)

Solution 10(iv)

Solution 10(v)

Solution 10(vi)

Solution 10(vii)

Solution 10(viii)

Solution 11

Solution 12

Solution 13

S i n c e space f open parentheses x close parentheses space i s space c o n t i n u o u s space a t space x equals 0 comma space L. H. L i m i t equals R. H. L i m i t.
T h u s comma space w e space h a v e
limit as x rightwards arrow 0 to the power of minus of f open parentheses x close parentheses equals limit as x rightwards arrow 0 to the power of plus of f open parentheses x close parentheses
rightwards double arrow limit as x rightwards arrow 0 to the power of minus of a sin pi over 2 open parentheses x plus 1 close parentheses equals limit as x rightwards arrow 0 to the power of plus of fraction numerator tan x minus sin x over denominator x cubed end fraction
rightwards double arrow a cross times 1 equals limit as x rightwards arrow 0 of fraction numerator tan x minus sin x over denominator x cubed end fraction
rightwards double arrow a equals limit as x rightwards arrow 0 of fraction numerator begin display style fraction numerator sin x over denominator cos x end fraction end style minus sin x over denominator x cubed end fraction
rightwards double arrow a equals limit as x rightwards arrow 0 of fraction numerator fraction numerator sin x over denominator x end fraction open parentheses begin display style fraction numerator 1 over denominator cos x end fraction end style minus 1 close parentheses over denominator x squared end fraction
rightwards double arrow a equals limit as x rightwards arrow 0 of fraction numerator fraction numerator sin x over denominator x end fraction open parentheses begin display style fraction numerator 1 minus cos x over denominator cos x end fraction end style close parentheses over denominator x squared end fraction
rightwards double arrow a equals limit as x rightwards arrow 0 of fraction numerator sin x over denominator x end fraction cross times limit as x rightwards arrow 0 of fraction numerator 1 over denominator cos x end fraction cross times limit as x rightwards arrow 0 of fraction numerator 1 minus cos x over denominator x squared end fraction
rightwards double arrow a equals 1 cross times 1 cross times limit as x rightwards arrow 0 of fraction numerator 1 minus cos x over denominator x squared end fraction
rightwards double arrow a equals limit as x rightwards arrow 0 of fraction numerator 1 minus cos x over denominator x squared end fraction cross times fraction numerator 1 plus cos x over denominator 1 plus cos x end fraction
rightwards double arrow a equals limit as x rightwards arrow 0 of fraction numerator 1 minus cos squared x over denominator x squared open parentheses 1 plus cos x close parentheses end fraction
rightwards double arrow a equals limit as x rightwards arrow 0 of fraction numerator sin squared x over denominator x squared open parentheses 1 plus cos x close parentheses end fraction
rightwards double arrow a equals limit as x rightwards arrow 0 of fraction numerator sin squared x over denominator x squared end fraction cross times limit as x rightwards arrow 0 of fraction numerator 1 over denominator 1 plus cos x end fraction
rightwards double arrow a equals 1 cross times limit as x rightwards arrow 0 of fraction numerator 1 over denominator 1 plus cos x end fraction
rightwards double arrow a equals 1 cross times fraction numerator 1 over denominator 1 plus 1 end fraction
rightwards double arrow a equals 1 half

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Solution 25

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Solution 26

Solution 27

Solution 28

Solution 29

Solution 30

Solution 31

Solution 32

Solution 33

Solution 34

Solution 35

Solution 36(i)

Solution 36(ii)

L e t space x minus 1 equals y
rightwards double arrow x equals y plus 1
T h u s comma space
limit as x rightwards arrow 1 of open parentheses x minus 1 close parentheses tan fraction numerator pi x over denominator 2 end fraction equals limit as y rightwards arrow 0 of y tan fraction numerator pi open parentheses y plus 1 close parentheses over denominator 2 end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals limit as y rightwards arrow 0 of y tan open parentheses fraction numerator pi y over denominator 2 end fraction plus pi over 2 close parentheses
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals minus limit as y rightwards arrow 0 of y c o t fraction numerator pi y over denominator 2 end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals minus limit as y rightwards arrow 0 of y fraction numerator cos fraction numerator pi y over denominator 2 end fraction over denominator sin fraction numerator pi y over denominator 2 end fraction end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals minus limit as y rightwards arrow 0 of y fraction numerator cos fraction numerator pi y over denominator 2 end fraction over denominator begin display style fraction numerator open parentheses sin fraction numerator pi y over denominator 2 end fraction close parentheses pi over 2 over denominator pi over 2 end fraction end style end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals minus limit as y rightwards arrow 0 of fraction numerator cos fraction numerator pi y over denominator 2 end fraction over denominator begin display style fraction numerator open parentheses sin fraction numerator pi y over denominator 2 end fraction close parentheses pi over 2 over denominator fraction numerator pi y over denominator 2 end fraction end fraction end style end fraction
space space space space space space space space space space space space space space space space space space space space space space space space equals minus limit as y rightwards arrow 0 of 2 over pi fraction numerator cos fraction numerator pi y over denominator 2 end fraction over denominator begin display style fraction numerator open parentheses sin fraction numerator pi y over denominator 2 end fraction close parentheses over denominator fraction numerator pi y over denominator 2 end fraction end fraction end style end fraction
space space space space space space space space space space space space space space space space space space space space space space space space equals minus 2 over pi limit as y rightwards arrow 0 of cos fraction numerator pi y over denominator 2 end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space equals minus 2 over pi
S i n c e space t h e space f u n c t i o n space i s space c o n t i n u o u s comma space L. H. L i m i t equals R. H. L i m i t
T h u s comma space k equals minus 2 over pi

Solution 36(iii)

Solution 36(iv)

Solution 36(v)

Solution 36(vi)

Solution 36(vii)

Solution 36(viii)

Solution 36(ix)

Solution 37

Solution 38

Solution 39(i)

Solution 39(ii)

Solution 40

Solution 41

Solution 42

Solution 43

Solution 44

Solution 45

Solution 46

RD Sharma Solution for Class 12 Science Mathematics Chapter 9 - Continuity Page/Excercise 9.2

Solution 1

Solution 2

Solution 3(i)

Solution 3(ii)

Solution 3(iii)

Solution 3(iv)

Solution 3(v)

Solution 3(vi)

Solution 3(vii)

Solution 3(viii)

Solution 3(ix)

Solution 3(x)

Solution 3(xi)

Solution 3(xii)

Solution 3(xiii)

Solution 4(i)

Solution 4(ii)

Solution 4(iii)

Solution 4(iv)

Solution 4(v)

Solution 4(vi)

Solution 4(vii)

Solution 4(viii)

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

RD Sharma Solution for Class 12 Science Mathematics Chapter 9 - Continuity Page/Excercise 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)

RD Sharma Solution for Class 12 Science Mathematics Chapter 9 - Continuity Page/Excercise 9VSAQ

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

TopperLearning provides step-by-step solutions for each question in each chapter in the RD Sharma textbook for class 9. Access the CBSE Class 9 Mathematics Chapter 9 - Continuity for free. The textbook questions have been solved by our subject matter experts to help you understand how to answer them. Our RD Sharma Textbook Solutions will help you to study and revise, and you can easily clear your fundamentals of Chapter 9 - Continuity.

Text Book Solutions

CBSE XII Science - Mathematics

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