Explanation Given information: f ( x , y , z ) = z x + y Concept used: From the liner approximation, L ( x , y , z ) = f ( a , b , c ) + f x ( a , b , c ) ( x − a ) + f y ( a , b , c ) ( y − b ) + f z ( a , b , c ) ( z − c ) Calculation: Consider, f ( x , y , c ) = z x + y So, f ( x , y , z ) at ( 8 , 4 , 5 ) f ( 8 , 4 , 5 ) = ( 5 ) 8 + 4 = 5 12 ... ( 1 ) Differentiating f ( x , y , z ) with respect to x we get, ∂ f ∂ x = ∂ ∂ x z x + y ⇒ ∂ f ∂ x = z ∂ ∂ x x + y ⇒ ∂ f ∂ x = z ( 1 2 x + y ) ⇒ ∂ f ∂ x = z 2 x + y So, f x ( x , y , z ) = z 2 x + y Hence f x ( x , y , z ) at ( 8 , 4 , 5 ) f x ( 8 , 4 , 5 ) = 5 2 8 + 4 = 5 2 12 ... ( 2 ) Differentiating f ( x , y , z ) with respect to y we get, ∂ f ∂ y = ∂ ∂ y z x + y ⇒ ∂ f ∂ y = z ∂ ∂ y x + y ⇒ ∂ f ∂ y = z ( 1 2 x + y ) ⇒ ∂ f ∂ y = z 2 x + y So, f y ( x , y , z ) = z 2 x + y Hence f y ( x , y , z ) at ( 8 , 4 , 5 ) f y ( 8 , 4 , 5 ) = 5 2 8 + 4 = 5 2 12 ..

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 14.4, Problem 21E

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linearization of f(x,y,z)=zx+y centered at (8,4,5)

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Chapter 14.4, Problem 20E

Chapter 14.4, Problem 22E

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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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Tofind: linearization of f ( x , y , z ) = z x + y centered at ( 8 , 4 , 5 )

Solution Summary: The author explains how the linearization of f(x,y,z) is centered at

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linearization of f(x,y,z)=zx+y centered at (8,4,5)

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Tofind: linearization of f ( x , y , z ) = z x + y centered at ( 8 , 4 , 5 )

Solution Summary: The author explains how the linearization of f(x,y,z) is centered at

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Tofind: linearization of f(x,y,z)=zx+y centered at (8,4,5)

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Chapter 14 Solutions

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linearization of f(x,y,z)=zx+y centered at (8,4,5)