Short Answer TypeFind the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm (b) r = 4 cm
Find the rate of change of the volume of a ball with respect to its radius r. How fast is the volume changing with respect to the radius when the radius is 2 m?
How fast is the volume of a ball changing with respect to its radius when the radius is 3 m?
A balloon which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the latter is 10 cm.
The cost function C(x), in rupees, of producing x items (x ≥ 15) in a certain factory is given by 
Determine the marginal cost function and the marginal cost of producing 100 items.
The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005 x3 - 0.02 x2 + 30 x + 5000.
Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.
Here C(x) = 0.005 x3 - 0.02 x2 + 30 x + 5000
Marginal cost = 
When x = 3, Marginal cost = 3 (0.005) (3)2 - 2 (0.02) (3) + 30
= 27(0.005) - 6 (0.02) + 30
=0.0135 - 0.12 + 30 = 30.015 = Rs. 30.02 nearly
The total revenue in Rupees received from the sale of x units of a product is given by
R(x) = 13x2 + 26x + 15.
Find the marginal revenue when x = 7.
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