Explanation Given information: f ( x , y ) = x 2 / ( y 2 + 1 ) Calculation: Consider, f ( x , y ) = x 2 / ( y 2 + 1 ) So, f ( x , y ) at ( 4 , 1 ) f ( 4 , 1 ) = ( 4 ) 2 / ( 1 2 + 1 ) = 16 2 = 8 ... ( 1 ) Differentiating f ( x , y ) with respect to x we get, ∂ f ∂ x = ∂ ∂ x x 2 / ( y 2 + 1 ) ⇒ ∂ f ∂ x = 1 ( y 2 + 1 ) ∂ ∂ x x 2 ⇒ ∂ f ∂ x = 1 ( y 2 + 1 ) ( 2 x ) ⇒ ∂ f ∂ x = 2 x y 2 + 1 So, f x ( x , y ) = 2 x y 2 + 1 Hence f x ( x , y ) at ( 4 , 1 ) f x ( 4 , 1 ) = 2 ( 4 ) ( 1 ) 2 + 1 = 8 2 = 4 ... ( 2 ) Differentiating f ( x , y ) with respect to y we get, ∂ f ∂ y = ∂ ∂ y x 2 / ( y 2 + 1 ) ⇒ ∂ f ∂ y = x 2 ∂ ∂ y 1 ( y 2 + 1 ) = x 2 ∂ ∂ y ( y 2 + 1 ) − 1

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Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 14.4, Problem 20E

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To estimate:

f(4.01,0.98) by using the linear approximation at an appropriate point (a,b).

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Chapter 14.4, Problem 19E

Chapter 14.4, Problem 21E

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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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To estimate: f ( 4.01 , 0.98 ) by using the linear approximation at an appropriate point ( a , b ) .

Solution Summary: The author calculates the value of f(4.01,0.98) by using the linear approximation at an appropriate point.

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To estimate:

f(4.01,0.98) by using the linear approximation at an appropriate point (a,b).

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Chapter 14 Solutions

To estimate: f ( 4.01 , 0.98 ) by using the linear approximation at an appropriate point ( a , b ) .

Solution Summary: The author calculates the value of f(4.01,0.98) by using the linear approximation at an appropriate point.

Videos

To estimate: f(4.01,0.98) by using the linear approximation at an appropriate point (a,b).

Want to see the full answer?

Chapter 14 Solutions

To estimate:

f(4.01,0.98) by using the linear approximation at an appropriate point (a,b).