Explanation Given: The given function is F = y 2 i ^ + ( 2 x y + e z ) j ^ + y e z k ^ Calculation: We know that F = y 2 i ^ + ( 2 x y + e z ) j ^ + y e z k ^ (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 , ∂ 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 = y 2 i ^ , l e t F 2 = 2 x y + e z and l e t F 3 = z 3 Solving for the partial derivatives as given in equation (II) ∂ F 1 ∂ y = ∂ ( y 2 ) ∂ y = 2 y ∂ F 2 ∂ x = ∂ ( 2 x y + e z ) ∂ x = 2 y ∂ F 1 ...

4th Edition

ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Question

Chapter 17.3, Problem 11E

To determine

Whether the function $F = y^{2} \hat{i} + (2 x y + e^{z}) \hat{j} + y e^{z} \hat{k}$ is conservative, hence find a potential function

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Chapter 17.3, Problem 10E

Chapter 17.3, Problem 12E

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Chapter 17 Solutions

EBK CALCULUS

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Knowledge Booster

Whether the function F = y 2 i ^ + ( 2 x y + e z ) j ^ + y e z k ^ is conservative, hence find a potential function

Solution Summary: The author explains that the given function is conservative, hence find a potential function.

Whether the function $F = y^{2} \hat{i} + (2 x y + e^{z}) \hat{j} + y e^{z} \hat{k}$ is conservative, hence find a potential function

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Chapter 17 Solutions

Whether the function F = y 2 i ^ + ( 2 x y + e z ) j ^ + y e z k ^ is conservative, hence find a potential function

Solution Summary: The author explains that the given function is conservative, hence find a potential function.

Whether the function F=y2i^+(2xy+ez)j^+yezk^ is conservative, hence find a potential function

Want to see the full answer?

Chapter 17 Solutions

Whether the function $F = y^{2} \hat{i} + (2 x y + e^{z}) \hat{j} + y e^{z} \hat{k}$ is conservative, hence find a potential function