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(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 r = 2.
(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 Δr. How can you approximate the resulting change in area ΔA if Δr is small? |
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