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...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.3, Problem 17E

To determine

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 16E

Chapter 17.3, Problem 18E

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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

Ch. 17.1 - Prob. 7E Ch. 17.1 - Prob. 8E Ch. 17.1 - Prob. 9E Ch. 17.1 - Prob. 10E Ch. 17.1 - Prob. 11E Ch. 17.1 - Prob. 12E Ch. 17.1 - Prob. 13E Ch. 17.1 - Prob. 14E Ch. 17.1 - Prob. 15E Ch. 17.1 - Prob. 16E Ch. 17.1 - Prob. 17E Ch. 17.1 - Prob. 18E Ch. 17.1 - Prob. 19E Ch. 17.1 - Prob. 20E Ch. 17.1 - Prob. 21E Ch. 17.1 - Prob. 22E Ch. 17.1 - Prob. 23E Ch. 17.1 - Prob. 24E Ch. 17.1 - Prob. 25E Ch. 17.1 - Prob. 26E Ch. 17.1 - Prob. 27E Ch. 17.1 - Prob. 28E Ch. 17.1 - Prob. 29E Ch. 17.1 - Prob. 30E Ch. 17.1 - Prob. 31E Ch. 17.1 - Prob. 32E Ch. 17.1 - Prob. 33E Ch. 17.1 - Prob. 34E Ch. 17.1 - Prob. 35E Ch. 17.1 - Prob. 36E Ch. 17.1 - Prob. 37E Ch. 17.1 - Prob. 38E Ch. 17.1 - Prob. 39E Ch. 17.1 - Prob. 40E Ch. 17.1 - Prob. 41E Ch. 17.1 - Prob. 42E Ch. 17.1 - Prob. 43E Ch. 17.1 - Prob. 44E Ch. 17.1 - Prob. 45E Ch. 17.1 - Prob. 46E Ch. 17.1 - Prob. 47E Ch. 17.1 - Prob. 48E Ch. 17.1 - Prob. 49E Ch. 17.1 - Prob. 50E Ch. 17.1 - Prob. 51E Ch. 17.1 - Prob. 52E Ch. 17.1 - Prob. 53E Ch. 17.1 - Prob. 54E Ch. 17.1 - 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Prob. 13E Ch. 17.3 - Prob. 14E Ch. 17.3 - Prob. 15E Ch. 17.3 - Prob. 16E Ch. 17.3 - Prob. 17E Ch. 17.3 - Prob. 18E Ch. 17.3 - Prob. 19E Ch. 17.3 - Prob. 20E Ch. 17.3 - Prob. 21E Ch. 17.3 - Prob. 22E Ch. 17.3 - Prob. 23E Ch. 17.3 - Prob. 24E Ch. 17.3 - Prob. 25E Ch. 17.3 - Prob. 26E Ch. 17.3 - Prob. 27E Ch. 17.3 - Prob. 28E Ch. 17.3 - Prob. 29E Ch. 17.3 - Prob. 30E Ch. 17.3 - Prob. 31E Ch. 17.3 - Prob. 32E Ch. 17.3 - Prob. 33E Ch. 17.3 - Prob. 34E Ch. 17.3 - Prob. 35E Ch. 17.4 - Prob. 1PQ Ch. 17.4 - Prob. 2PQ Ch. 17.4 - Prob. 3PQ Ch. 17.4 - Prob. 4PQ Ch. 17.4 - Prob. 5PQ Ch. 17.4 - Prob. 6PQ Ch. 17.4 - Prob. 1E Ch. 17.4 - Prob. 2E Ch. 17.4 - Prob. 3E Ch. 17.4 - Prob. 4E Ch. 17.4 - Prob. 5E Ch. 17.4 - Prob. 6E Ch. 17.4 - Prob. 7E Ch. 17.4 - Prob. 8E Ch. 17.4 - Prob. 9E Ch. 17.4 - Prob. 10E Ch. 17.4 - Prob. 11E Ch. 17.4 - Prob. 12E Ch. 17.4 - Prob. 13E Ch. 17.4 - Prob. 14E Ch. 17.4 - Prob. 15E Ch. 17.4 - Prob. 16E Ch. 17.4 - Prob. 17E Ch. 17.4 - Prob. 18E Ch. 17.4 - Prob. 19E Ch. 17.4 - Prob. 20E Ch. 17.4 - 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Knowledge Booster

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?

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?

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?