Solved: (a) Find the average rate of change of the area of a circle with respect to its
Chapter 3, Problem 3.7.13(choose chapter or problem)
(a) Find the average rate of change of the area of a circle with respect to its radius as changes from (i) 2 to 3 (ii) 2 to 2.5 (iii) 2 to 2.1 (b) Find the instantaneous rate of change when . (c) Show that the rate of change of the area of a circle with respect to its radius (at any ) is equal to the circumference of the circle. Try to explain geometrically why this is true by drawing a circle whose radius is increased by an amount . How can you approximate the resulting change in area if is small?
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