Chapter 13 Derivative as a Rate Measurer Ex 13.1

Question 1

Solution 1

Question 2

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Question 3

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Question 4

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Question 5

Find the rate of change of the volume of a cone with respect to the radius of its base.Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

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Question 9

Solution 9

Question 10

The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (Marginal revenue). If the total revenue (in rupees) received from the sale of x units of a product is given by R(x) = 3x² + 36x + 5, find the marginal revenue, when x=5, and write which value does the question indicate.Solution 10

Chapter 13 Derivative as a Rate Measurer Ex. 13.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

The radius of a spherical soap bubble is increasing at the rate of 0.2 cm/sec. Find the rate of increase of its surface area, when the radius is 7 cm.Solution 5

Question 6

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Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

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Question 12

Solution 12

Question 13

Solution 13

Question 14

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Question 15

Solution 15

Question 16(i)

Find an angle θ, which increases twice as fast as its cosine.Solution 16(i)

Question 16(ii)

Find the angle θ

Whose rate of increase is twice the rate of decrease of its consine.Solution 16(ii)

Question 17

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Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

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Question 23

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Question 24

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Question 25

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Question 26

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Question 27

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Question 28

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Question 29

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Question 30

Solution 30

Question 31

Solution 31