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Which of the following functions is a potential function for the conservative vector field F(x, y, z) = (2-4, 2³ - 2y, x + 3yz²)?

Which of the following functions is a potential function for the conservative vector field F(x, y, z) = (2-4, 2³ - 2y, x + 3yz²)?

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.FOM: Focus On Modeling: Vectors Fields
Problem 16P
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Which of the following functions is a potential function for the conservative vector field F (x, y, z) = (z − 4, z³ – 2y, x + 3yz² )? ○ ¢ (x, y, z) = x² + y² + z² (x, y, z) = xz − y² + yz³ – 4x ○ p(x, y, z) = xz+ y² − yz³ – 4x None of the given choices ○ (x, y, z) =−xz+y²-yz³ + 4x
Transcribed Image Text:Which of the following functions is a potential function for the conservative vector field F (x, y, z) = (z − 4, z³ – 2y, x + 3yz² )? ○ ¢ (x, y, z) = x² + y² + z² (x, y, z) = xz − y² + yz³ – 4x ○ p(x, y, z) = xz+ y² − yz³ – 4x None of the given choices ○ (x, y, z) =−xz+y²-yz³ + 4x
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