Explanation Given information: f ( x , y , z ) = x y / z 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 , z ) = x y / z So, f ( x , y , z ) at ( 2 , 1 , 2 ) f ( 2 , 1 , 2 ) = ( 2 ) ( 1 ) 2 = 1 ... ( 1 ) Differentiating f ( x , y , z ) with respect to x we get, ∂ f ∂ x = ∂ ∂ x x y z ⇒ ∂ f ∂ x = y z ∂ ∂ x x ⇒ ∂ f ∂ x = y z So, f x ( x , y , z ) = y z Hence f x ( x , y , z ) at ( 2 , 1 , 2 ) f x ( 2 , 1 , 2 ) = 1 2 ... ( 2 ) Differentiating f ( x , y , z ) with respect to y we get, ∂ f ∂ y = ∂ ∂ y x y z ⇒ ∂ f ∂ y = x z ∂ ∂ y y ⇒ ∂ f ∂ y = x z f y ( x , y , z ) = x z So, f y ( 2 , 1 , 2 ) = 2 2 = 1 Hence f y ( x , y , z ) at ( 2 , 1 , 2 ) f y ( 2 , 1 , 2 ) = 2 2 = 1 ... ( 3 ) Differentiating f ( x , y , z ) with respect to z we get, ∂ f ∂ z = ∂ ∂ z x y z ⇒ ∂ f ∂ z = x y ∂ ∂ z 1 z = x y ∂ ∂ z z − 1 ⇒ ∂ f ∂ z = x y ( − 1 z 2 ) ⇒ ∂ f ∂ z = − x y z 2 So, f z ( x , y , z ) = − x y z 2 Hence f z ( x , y , z ) at ( 2 , 1 , 2 ) f z ( 2 , 1 , 2 ) = − ( 2 ) ( 1 ) ( 2 ) 2 = − 1 2

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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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 22E

To determine

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linearization of f(x,y,z)=xy/z centered at (2,1,2), we have estimate f(2.05,0.9,2.01) and compare the value obtained from calculator.

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Chapter 14.4, Problem 21E

Chapter 14.4, Problem 23E

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Chapter 14 Solutions

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Tofind: linearization of f ( x , y , z ) = x y / z centered at ( 2 , 1 , 2 ) , we have estimate f ( 2.05 , 0.9 , 2.01 ) and compare the value obtained from calculator.

Solution Summary: The author compares the linearization of f(x,y,z)=xy/z with the value obtained from calculator.

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Tofind:

linearization of f(x,y,z)=xy/z centered at (2,1,2), we have estimate f(2.05,0.9,2.01) and compare the value obtained from calculator.

Want to see the full answer?

Chapter 14 Solutions

Tofind: linearization of f ( x , y , z ) = x y / z centered at ( 2 , 1 , 2 ) , we have estimate f ( 2.05 , 0.9 , 2.01 ) and compare the value obtained from calculator.

Solution Summary: The author compares the linearization of f(x,y,z)=xy/z with the value obtained from calculator.

Concept explainers

Videos

Tofind: linearization of f(x,y,z)=xy/z centered at (2,1,2), we have estimate f(2.05,0.9,2.01) and compare the value obtained from calculator.

Want to see the full answer?

Chapter 14 Solutions

Tofind:

linearization of f(x,y,z)=xy/z centered at (2,1,2), we have estimate f(2.05,0.9,2.01) and compare the value obtained from calculator.