Chapter 3.9, Problem 40E

To determine

(a)

The reason for which $V\left(h+\Delta h\right)-V\left(h\right)\approx A\left(h\right)\Delta h$ if $\Delta h$ is small.

To determine

(b)

To prove:

That $\frac{dV}{dh}=A\left(h\right)$ using the expression $V\left(h+\Delta h\right)-V\left(h\right)\approx A\left(h\right)\Delta h$.

To determine

(c)

To prove:

That the water level $h$ decreases at a constant rate.