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Test: Rate of Change And Approximations - Question 1

The radius of air bubble is increasing at the rate of 0. 25 cm/s. At what rate the volume of the bubble is increasing when the radius is 1 cm.

Test: Rate of Change And Approximations - Question 2

The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 5x^{2} + 22x + 35^{. }Find the marginal revenue, when x = 7, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant

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Test: Rate of Change And Approximations - Question 3

Find the approximate change in total surface area of a cube of side x metre caused by increase in side by 1%.

Test: Rate of Change And Approximations - Question 4

The volume of cube is increasing at the constant rate of 3 cm^{3}/s. Find the rate of change of edge of the cube when its edge is 5 cm.

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Test: Rate of Change And Approximations - Question 5

The total cost associated with the production of x units of a product is given by C(x) = 5x^{2} + 14x + 6. Find marginal cost when 5 units are produced

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Test: Rate of Change And Approximations - Question 6

At a distance of 120ft from the foot of a tower the elevation of its top is 60o. If the possible error in measuring the distance and elevation are 1 inch and 1 minute, find approximate error in calculated height.

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Test: Rate of Change And Approximations - Question 7

A stone is dropped into a quiet lake and waves move in circles at a speed of 2cm per second. At the instant, when the radius of the circular wave is 12 cm, how fast is the enclosed area changing ?

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Test: Rate of Change And Approximations - Question 9

Find the approximate value of f(10.01) where f(x) = 5x^{2} +6x + 3

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Test: Rate of Change And Approximations - Question 10

Given a function y = f(x) . Let Δx be the very small change in the value of x , then the corresponding change in the value of y that is Δy is approximately given by

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