Explanation Given: f ( x , y ) = x ( 1 + y ) − 1 ( a , b ) = ( 8 , 1 ) . Formula used: The linearization of a function f ( x , y ) at ( a , b ) is L ( x , y ) = f ( a , b ) + f x ( a , b ) ( x − a ) + f y ( a , b ) ( y − b ) f ( a + h , b + k ) ≈ L ( x , y ) = f ( a , b ) + f x ( a , b ) h + f y ( a , b ) k Partial derivative of a function f ( x , y ) with respect to x is calculated by doing derivative of that function treating y as constant. Similarly partial derivative of a function f ( x , y ) with respect to y is calculated by doing derivative of that function treating x as constant. f x ( a , b ) = δ f ( x , y ) δ x at ( a , b ) f y ( a , b ) = δ f ( x , y ) δ y at ( a , b ) d d y ( 1 a + b y ) = − b ( a + b y ) 2 Calculation: f ( x , y ) = x ( 1 + y ) − 1 f ( 8 , 1 ) = 8 ( 1 + 1 ) − 1 = 4 f x ( x , y ) = δ f ( x , y ) δ x = ( 1 +...

3rd Edition

ISBN: 9781464114885

Author: Jon Rogawski, Colin Adams

Publisher: W. H. Freeman

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Question

Chapter 14.4, Problem 14E

To determine

To find: linearization $L (x, y)$ of a function $f (x, y) = x {(1 + y)}^{- 1}$ at $(a, b) = (8, 1)$ .

Also use it to estimate $\frac{7.98}{2.02}$ and compare with value obtained using calculator.

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Chapter 14.4, Problem 13E

Chapter 14.4, Problem 15E

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Chapter 14 Solutions

Calculus: Early Transcendentals

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

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linearization L ( x , y ) of a function f ( x , y ) = x ( 1 + y ) − 1 at ( a , b ) = ( 8 , 1 ) . Also use it to estimate 7.98 2.02 and compare with value obtained using calculator.

To find: linearization L(x,y) of a function f(x,y)=x(1+y)−1 at (a,b)=(8,1). Also use it to estimate 7.982.02 and compare with value obtained using calculator.

Want to see the full answer?

Chapter 14 Solutions

To find: linearization $L (x, y)$ of a function $f (x, y) = x {(1 + y)}^{- 1}$ at $(a, b) = (8, 1)$ .

Also use it to estimate $\frac{7.98}{2.02}$ and compare with value obtained using calculator.