The wave heights in the open sea depend on the speed v of the wind and the length of time that the wind has been blowing at that speed. Values of the function h = ƒ(v, t) are recorded in feet in the following table.
Duration (hours)
Wind speed (knots)
v t
5
10
15
20
30
40
50
2
4
7
8
9
13
16
17
18
19
14
21
25
28
31
33
29
36
45
48
60
24
37
47
54
62
67
69
(a) What are the meanings of the partial derivatives ∂h/∂v and ∂h/∂t?
(b) Estimate the values of ƒv(40, 15) and ƒt(40, 50). What are the practical interpretations of these values?
(c) What appears to be the value of the following limit?
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