Explanation Given information: The given field is F = 〈 y z , x z , x y 〉 . Concept used: We use concept of finding potential function. A function f ( x , y , z ) is said to be a potential function of the vector field F = 〈 f 1 , f 2 , f 3 〉 if it satisfies f ( x , y , z ) = ∫ f 1 d x , f ( x , y , z ) = ∫ f 2 d y , f ( x , y , z ) = ∫ f 3 d z Calculation: As given F = 〈 y z , x z , x y 〉 , so its potential function can be given as f ( x , y , z ) = ∫ y z d x = x y z + h 1 ( y , z ) , f ( x , y , z ) = ∫ x z d y = x y z + h 2 ( x , z ) ,

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Domain

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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Question

Chapter 17.1, Problem 4PQ

To determine

To show: The potential function of F=〈yz,xz,yz〉 is given by f(x,y,z)=xyz and also find another potential function.

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Chapter 17.1, Problem 3PQ

Chapter 17.1, Problem 1E

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Chapter 17 Solutions

CALCULUS (CLOTH)

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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The potential function of F = 〈 y z , x z , y z 〉 is given by f ( x , y , z ) = x y z and also find another potential function.

Solution Summary: The author explains that the potential function of F=langle yz,xz and varphi is f(x,y,z).

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To show: The potential function of F=〈yz,xz,yz〉 is given by f(x,y,z)=xyz and also find another potential function.

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Chapter 17 Solutions