   Chapter 14.3, Problem 2E

Chapter
Section
Textbook Problem

At the beginning of this section we discussed the function I = f(T, H), where I is the heat index, T is the temperature, and H is the relative humidity. Use Table 1 to estimate fT(92, 60) and fH(92, 60). What are the practical interpretations of these values?Table 1 Heat index I as a function of temperature and humidity To determine

To estimate: The values of fT(92,60) and fH(92,60) from the Table 1, interpret the values.

Explanation

Given:

The function I=f(T,H) , where I is the heat index, T is the temperature and H is the relative humidity.

Definition used:

“If f is a function of two variables, its partial derivatives are the functions fx and fy defined by

fx(x,y)=limh0f(x+h,y)f(x,y)hfy(x,y)=limh0f(x,y+h)f(x,y)h

Calculation:

Obtain fT(92,60) by definition.

fT(92,60)=limh0f(92+h,60)f(92,60)h

Assume h=2 and obtain the value of fT(92,60) .

fT(92,60)f(92+2,60)f(92,60)2f(94,60)f(92,60)2=1111052=62=3

Similarly, assume h=2 and use Table 1 to obtain the values of fT(92,60) .

fT(92,60)f(922,60)f(92,60)2f(90,60)f(92,60)2=1001052=52=2.5

Obtain the average of above two values of fT(92,60) ,

fT(92,60)=3+522=6+522=1122=114

Thus, the value of fT(92,60)=2

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