Explanation Given: F = 〈 x , 0 〉 G = 〈 y , 0 〉 Formula used: If f is a potential function for the vector field F → then F → = ∇ → f For a vector field to have a potential function it should be conservative i.e. curl of the vector field should be 0. Calculation: F = 〈 x , 0 〉 F → = ∇ → f = 〈 ∂ f ∂ x , ∂ f ∂ y 〉 ⇒ ∂ f ∂ x = x ⇒ f = x 2 2 + h ( y ) ∂ f ∂ y = 0 = d h d y ⇒ h = c ⇒ f = x 2 2 + c If G → = 〈 P , Q 〉 is a conservative vector field where potential function is g G → =

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.1, Problem 38E

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A potential function for $F = 〈 x, 0 〉$ using inspection and prove that $G = 〈 y, 0 〉$ is not conservative.

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Chapter 17.1, Problem 37E

Chapter 17.1, Problem 39E

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Chapter 17 Solutions

CALCULUS (CLOTH)

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A potential function for F = 〈 x , 0 〉 using inspection and prove that G = 〈 y , 0 〉 is not conservative.

Solution Summary: The author determines a potential function for F = x, 0 and proves that G is not conservative.

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A potential function for $F = 〈 x, 0 〉$ using inspection and prove that $G = 〈 y, 0 〉$ is not conservative.

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Chapter 17 Solutions

A potential function for F = 〈 x , 0 〉 using inspection and prove that G = 〈 y , 0 〉 is not conservative.

Solution Summary: The author determines a potential function for F = x, 0 and proves that G is not conservative.

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A potential function for F=〈x,0〉 using inspection and prove that G=〈y,0〉 is not conservative.

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Chapter 17 Solutions

A potential function for $F = 〈 x, 0 〉$ using inspection and prove that $G = 〈 y, 0 〉$ is not conservative.