Explanation Given information: The given vector field is F = 〈 x 2 x 2 + y 2 , y 2 x 2 + y 2 〉 . Formula used: Potential function of a vector field F = 〈 F 1 ( x , y ) , F 2 ( x , y ) 〉 will exist if ∂ F 1 ∂ y − ∂ F 2 ∂ x = 0 That is if F is conservative. Potential function for the vector field F = 〈 F 1 ( x , y ) , F 2 ( x , y ) 〉 is given by a function f such that F = 〈 F 1 ( x , y ) , F 2 ( x , y ) 〉 = ∇ f Where ∇ f = 〈 f x , f y 〉 Calculation: Consider the given vector field. F = 〈 x 2 x 2 + y 2 , y 2 x 2 + y 2 〉 Here, F 1 ( x , y ) = x 2 x 2 + y 2 , and F 2 ( x , y ) = y 2 x 2 + y 2 Now check whether F is conservative or not

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Chapter 16.3, Problem 33E

To determine

To find:

A potential function for the given vector field if it exists.

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Chapter 16.3, Problem 32E

Chapter 16.3, Problem 34E

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Chapter 16 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

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A potential function for the given vector field if it exists.

Solution Summary: The author explains the formula used to find a potential function for the given vector field.

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To find: A potential function for the given vector field if it exists.

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Chapter 16 Solutions

To find:

A potential function for the given vector field if it exists.