Explanation Given: Function is given b y F = 〈 e x ( z + 1 ) , − cos y , e x 〉 Calculation: We know that F = 〈 e x ( z + 1 ) , − cos y , e x 〉 (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 onl y 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 = e x ( z + 1 ) , l e t F 2 = − cos y and l e t F 3 = e x Solving for the partial derivatives as given in equation (II) ∂ F 1 ∂ y = ∂ ( e x ( z + 1 ) ) ∂ y = 0 ∂ F 2 ∂ x = ∂ ( − cos y ) ∂ x = 0 ð ∂ F 1 ∂ y = ∂ F 2 ∂ x (III) ∂ F 2 ∂ z = ∂ ( − cos y ) ∂ z = 0 ∂ F 3 ∂ y = ∂ ( e x ) ∂ y = 0 ð ∂ F 2 ∂ z = ∂ F 3 ∂ y (IV) ∂ F 3 ∂ x = ∂ ( e x ) ∂ x = e x ∂ F 1 ∂ z = ∂ ( e x ( z + 1 ) ) ∂ z = e x 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 16E

To determine

Whether the function $F = 〈 e^{x} (z + 1), - \cos y, e^{x} 〉$ is conservative, hence find a potential function

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Chapter 17.3, Problem 15E

Chapter 17.3, Problem 17E

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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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Knowledge Booster

Whether the function F = 〈 e x ( z + 1 ) , − cos y , e x 〉 is conservative, hence find a potential function

Solution Summary: The author explains that the given function is conservative if it proves the following condition.

Whether the function $F = 〈 e^{x} (z + 1), - \cos y, e^{x} 〉$ is conservative, hence find a potential function

Want to see the full answer?

Chapter 17 Solutions

Whether the function F = 〈 e x ( z + 1 ) , − cos y , e x 〉 is conservative, hence find a potential function

Solution Summary: The author explains that the given function is conservative if it proves the following condition.

Whether the function F=〈ex(z+1),−cosy,ex〉 is conservative, hence find a potential function

Want to see the full answer?

Chapter 17 Solutions

Whether the function $F = 〈 e^{x} (z + 1), - \cos y, e^{x} 〉$ is conservative, hence find a potential function