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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)?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
If C is any sectionally smooth curve, which of the following line integrals is NOT path-independent? None of the given choices Of dx + 3y² dy + 2zdz Ofc (yz - x) dx + (xz − y)dy + (xy – z)dz Ofe (by-2a) dx + (ax + 3)dy, a 0 Scyzdx + x² dy + xzdz
Transcribed Image Text:If C is any sectionally smooth curve, which of the following line integrals is NOT path-independent? None of the given choices Of dx + 3y² dy + 2zdz Ofc (yz - x) dx + (xz − y)dy + (xy – z)dz Ofe (by-2a) dx + (ax + 3)dy, a 0 Scyzdx + x² dy + xzdz
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