(Solved): (a) Use the formula for the area of a circle of radius \( r, A=\pi r^{2} \), to find \( \frac{d A} ...

(a) Use the formula for the area of a circle of radius \( r, A=\pi r^{2} \), to find \( \frac{d A}{d r} \). \( \frac{d A}{d r}=1 \) (b) The result from part (a) should look familiar. What does \( \frac{d A}{d r} \) represent geometrically? \( \frac{d A}{d r} \) represents: (c) Use the difference quotient to explain the observation you made in part (b). For small \( h, A^{\prime}(r) \approx \frac{A(r+h)-A(r)}{h} \). When \( h>0 \), the numerator of \( A^{\prime}(r) \) represents: As \( h \) approaches \( 0, A^{\prime} \) can be approximated by: