Problem 13E

13. (a) Find the average rate of change of the area of a circle with respect to its radius $r$ as $r$ 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 $r$ ) 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 $\Delta r .$ How can you approximate the resulting change in area $\Delta A$ if $\Delta r$ is small?

 

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