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. Consider the vector field F = (y cos(ry), x cos(ry), – sin(z)). (a) Show that F is conservative. (b) Find a potential function f such that F = Vf. (c) Let C be the curve parametrised by r(t) = (cos t, sin t, 3+sin t) between the points (0, –1, 2) and (0,1, 4). Evaluate F- dr.

. Consider the vector field F = (y cos(ry), x cos(ry), – sin(z)). (a) Show that F is conservative. (b) Find a potential function f such that F = Vf. (c) Let C be the curve parametrised by r(t) = (cos t, sin t, 3+sin t) between the points (0, –1, 2) and (0,1, 4). Evaluate F- dr.

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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8. Consider the vector field F = (y cos(ry), x cos(xy), – sin(z)). (a) Show that F is conservative. (b) Find a potential function f such that F = Vf. (c) Let C be the curve parametrised by r(t) = (cost, sin t,3+sin t) between the points (0, –1, 2) and (0, 1,4). Evaluate F. dr.
Transcribed Image Text:8. Consider the vector field F = (y cos(ry), x cos(xy), – sin(z)). (a) Show that F is conservative. (b) Find a potential function f such that F = Vf. (c) Let C be the curve parametrised by r(t) = (cost, sin t,3+sin t) between the points (0, –1, 2) and (0, 1,4). Evaluate F. dr.
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