   Chapter 14.3, Problem 4E

Chapter
Section
Textbook Problem

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 ∂h/∂v and ∂h/∂t?(b) Estimate the values of fv(40, 15) and ft(40, 15). What are the practical interpretations of these values?(c) What appears to be the value of the following limit? lim t → ∞ ∂ h ∂ t

(a)

To determine

To explain: The meaning of the first order partial derivatives hv and ht where h=f(v,t) .

Explanation

The given function is h=f(v,t) , where h is the wave height, t is the length of time and v is the wind speed.

The partial derivative h

(b)

To determine

To estimate: The values of fv(40,15) and ft(40,15) from the given table and interpret the values.

(c)

To determine

To find: The value of limtht .

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