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a) Is the vector field F = (sin z, y², x cos z) conservative? Explain your reasoning. b) Compute the work done by the vector field F 1 (sin z, y², t cos z) when moving a particle from the point (2, 0, 0) to the point (-2, 0, 37) along the helical path č(t) = (2 cos t, 2 sint, t).

a) Is the vector field F = (sin z, y², x cos z) conservative? Explain your reasoning. b) Compute the work done by the vector field F 1 (sin z, y², t cos z) when moving a particle from the point (2, 0, 0) to the point (-2, 0, 37) along the helical path č(t) = (2 cos t, 2 sint, t).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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a) Is the vector field F = (sin z, y², x cos z) conservative? Explain your reasoning. b) Compute the work done by the vector field F = (sin z, y², t cos z) when moving a particle from the point (2, 0, 0) to the point (-2, 0, 3π) along the helical path č(t) = (2 cos t, 2 sin t, t).
Transcribed Image Text:a) Is the vector field F = (sin z, y², x cos z) conservative? Explain your reasoning. b) Compute the work done by the vector field F = (sin z, y², t cos z) when moving a particle from the point (2, 0, 0) to the point (-2, 0, 3π) along the helical path č(t) = (2 cos t, 2 sin t, t).
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