Explanation Given information: The given vector field is F = 〈 y , x 〉 . 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 = 〈 y , x 〉 Here, F 1 ( x , y ) = y and F 2 ( x , y ) = x Now check whether F is conservative or not. ∂ F 1 ∂ y − ∂ F 2 ∂ x = ∂ ( y ) ∂ y − ∂ ( x ) ∂ x = 1 − 1 = 0 Therefore, F is conservative vector field

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Chapter 16.1, Problem 40E

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To find:

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

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Chapter 16.1, Problem 39E

Chapter 16.1, Problem 41E

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Chapter 16 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E

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

Solution Summary: The author explains how to find a potential function for the given vector field if it exists.

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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.