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?