   Chapter 14, Problem 12RE

Chapter
Section
Textbook Problem

Find a linear approximation to the temperature function T(x, y) in Exercise 11 near the point (6, 4). Then use it to estimate the temperature at the point (5, 3.8). To determine

To find: The linearzation of the temperature function T(x,y) near the point (6,4) , use this approximation and approximate the value of T(x,y) at the point (5,3.8) .

Explanation

Given:

The function is, T(x,y) .

The values of Tx(6,4)3.5andTy(6,4)3.0 .

Calculation:

The linear approximation of the function T(x,y) at (6,4) is defined as,

T(6,4)T(6,4)+Tx(6,4)(x6)+Ty(6,4)(y4) (1)

Substitute the respective values in the equation (1) and find the linear approximation,

T(6,4)T(6,4)+Tx(6,4)(x6)+Ty(6,4)(y4)T(6,4)80+3

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