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# (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 $\space \space \space$ (ii) 2(0 2.5 $\space \space \space$ (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?

## a) $5 \pi, 4.5 \pi, 4.1 \pi$b) 4$\pi$c) $\Delta A \approx(2 \pi r \Delta r),$ when $\Delta r$ is small

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Oregon State University

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