Exercise 4

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 \(h = f(v, t)\) are recorded in feet in the following table.

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

  1. Estimate the values of \(f_t(40, 15)\) and \(f_t(40, 15)\). What are the practical interpretations of these values?

  2. What appears to be the value of the following limit?

\[ \lim_{t \to \infty} \frac{\partial h}{\partial t} \]