Chapter 14.3, Problem 4E

The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function $h=f\left(v,t\right)$ are recorded in feet in the following table.

Duration (hours)
Wind speed (knots)	v\t	5	10	15	20	30	40	50
	10	2	2	2	2	2	2	2
	15	4	4	5	5	5	5	5
	20	5	7	8	8	9	9	9
	30	9	13	16	17	18	19	19
	40	14	21	25	28	31	33	33
	50	19	29	36	40	45	48	50
	60	24	37	47	54	62	67	69

(a) What are the meanings of the partial derivatives $\partial h/\partial v$ and $\partial h/\partial t$?

(b) Estimate the values of $f_v\left(40,15\right)$ and $f_t\left(40,15\right)$. What are the practical interpretations of these values?

(c) What appears to be the value of the following limit?

$\underset{t\to \infty }{\lim }\frac{\partial h}{\partial t}$