Explanation Given: the given function is given by F = 〈 2 x y + 5 , x 2 − 4 z , − 4 y 〉 Calculation: We know that F = 〈 2 x y + 5 , x 2 − 4 z , − 4 y 〉 (I) F can be is conservative if it proves the following condition | i j k ∂ ∂ x ∂ ∂ y ∂ ∂ z F 1 F 2 F 3 | = 0 Which implies that F is conservative if and only if the following conditions are met ∂ F 1 ∂ y = ∂ F 2 ∂ x And ∂ F 2 ∂ z = ∂ F 3 ∂ y And ∂ F 3 ∂ x = ∂ F 1 ∂ z (II) In the given function from equation (I) l e t F 1 = 2 x y + 5 , l e t F 2 = x 2 − 4 z and l e t F 3 = − 4 y Solving for the partial derivatives as given in equation (II) ∂ F 1 ∂ y = ∂ ( 2 x y + 5 ) ∂ y = 2 x ∂ F 2 ∂ x = ∂ ( x 2 − 4 z ) ∂ x = 2 x ð ∂ F 1 ∂ y = ∂ F 2 ∂ x (III) ∂ F 2 ∂ z = ∂ ( x 2 − 4 z ) ∂ z = − 4 ∂ F 3 ∂ y = ∂ ( − 4 y ) ∂ y = − 4 ð ∂ F 2 ∂ z = ∂ F 3 ∂ y (IV) ∂ F 3 ∂ x = ∂ ( − 4 y ) ∂ x = 0 ∂ F 1 ∂ z = ∂ ( 2 x y + 5 ) ∂ z = 0 ð ∂ F 3 ∂ x = ∂ F 1 ∂ z (V) From equation (III), (IV) and (V) It is proved that F is conservation...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 17.3, Problem 15E

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Whether the function $F = 〈 2 x y + 5, x^{2} - 4 z, - 4 y 〉$ is conservative, hence find a potential function?

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Chapter 17.3, Problem 14E

Chapter 17.3, Problem 16E

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Chapter 17 Solutions

Calculus - Standalone book

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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Whether the function F = 〈 2 x y + 5 , x 2 − 4 z , − 4 y 〉 is conservative, hence find a potential function?

Solution Summary: The author explains that the given function is conservative, hence find a potential function. F can be conservative if the following conditions are met.

Whether the function $F = 〈 2 x y + 5, x^{2} - 4 z, - 4 y 〉$ is conservative, hence find a potential function?

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Chapter 17 Solutions

Whether the function F = 〈 2 x y + 5 , x 2 − 4 z , − 4 y 〉 is conservative, hence find a potential function?

Solution Summary: The author explains that the given function is conservative, hence find a potential function. F can be conservative if the following conditions are met.

Whether the function F=〈2xy+5,x2−4z,−4y〉 is conservative, hence find a potential function?

Want to see the full answer?

Chapter 17 Solutions

Whether the function $F = 〈 2 x y + 5, x^{2} - 4 z, - 4 y 〉$ is conservative, hence find a potential function?