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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v). The following table of values is an excerpt from Table 1 in Section 14.1. Use the table to find a linear approximation to the wind-chill index function when T is near − 15°C and v is near 50 km/h. Then estimate the wind-chill index when the temperature is −17°C and the wind speed is 55 km/h.

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To determine

To find: The linear approximation of the wind-chill index function W=f(T,v) at actual temperature near 15C and the wind speed is near 50km/h , use this approximation and approximate the value of f(T,v)=f(17,55) .

Explanation

Given:

The function is, W=f(T,v) where T is actual temperature, v is wind speed.

Calculation:

The linear approximation of the function W=f(T,v) at (15,50) is defined as,

f(15,50)f(15,50)+fT(15,50)(T+15)+fv(15,50)(v50) . (1)

The value of fT(15,50) is defined as, fT(15,50)=limh0f(15+h,50)f(15,50)h

Let h=5 in the above equation,

fT(15,50)=limh0f(15+5,50)f(15,50)5=limh0f(10,50)f(15,50)5=22+295=1.4

Let h=5 and find fT(15,50) ,

fT(15,50)=limh0f(155,50)f(15,50)5=limh0f(20,50)f(15,50)5=27+295=1.2

Compute the average value of, fT(15,50)=1.4 and fT(15,50)=1.2 .

fT(15,50)=1.4+1.22=2.62=1.3

Thus, the value of fT(15,50)=1.3 .

Similarly, the function fv(15,50) is defined as, fv(15,50)=limh0f(15,50+h)f(15,50)h .

Let h=10 and use table to find fv(15,50) .

fv(15,50)=limh0f(15,50+10)f(15,50)10=limh0f(15,60)f(15,50)10=30+2910=0

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Chapter 14 Solutions

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P-14RECh-14 P-15RECh-14 P-16RECh-14 P-17RECh-14 P-18RECh-14 P-19RECh-14 P-20RECh-14 P-21RECh-14 P-22RECh-14 P-23RECh-14 P-24RECh-14 P-25RECh-14 P-26RECh-14 P-27RECh-14 P-28RECh-14 P-29RECh-14 P-30RECh-14 P-31RECh-14 P-32RECh-14 P-33RECh-14 P-34RECh-14 P-35RECh-14 P-36RECh-14 P-37RECh-14 P-38RECh-14 P-39RECh-14 P-40RECh-14 P-41RECh-14 P-42RECh-14 P-43RECh-14 P-44RECh-14 P-45RECh-14 P-46RECh-14 P-47RECh-14 P-48RECh-14 P-49RECh-14 P-50RECh-14 P-51RECh-14 P-52RECh-14 P-53RECh-14 P-54RECh-14 P-55RECh-14 P-56RECh-14 P-57RECh-14 P-58RECh-14 P-59RECh-14 P-60RECh-14 P-61RECh-14 P-62RECh-14 P-63RECh-14 P-64RECh-14 P-65RECh-14 P-1PCh-14 P-2PCh-14 P-3PCh-14 P-4PCh-14 P-5PCh-14 P-6PCh-14 P-7PCh-14 P-8P

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