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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
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).

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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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Chapter 14 Solutions

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