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. Consider the vector field F = (yze*z, etz , xye"=). (a) Show that F is conservative. (b) Find a potential function ƒ such that F = Vƒ. %3D (c) Let C be the portion of the helix parametrised r(t) = (sin(t), cos(t), t) between the points (0, –1, –7) and (0, –1, 7). Evaluate F. dr .

. Consider the vector field F = (yze*z, etz , xye"=). (a) Show that F is conservative. (b) Find a potential function ƒ such that F = Vƒ. %3D (c) Let C be the portion of the helix parametrised r(t) = (sin(t), cos(t), t) between the points (0, –1, –7) and (0, –1, 7). 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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7. Consider the vector field F = (yze*z, ez , xye"z). (a) Show that F is conservative. (b) Find a potential function f such that F = Vf. (c) Let C be the portion of the helix parametrised r(t) = (sin(t), cos(t), t) between the points (0, –1, –7) and (0, –1, 7). Evaluate F. dr .
Transcribed Image Text:7. Consider the vector field F = (yze*z, ez , xye"z). (a) Show that F is conservative. (b) Find a potential function f such that F = Vf. (c) Let C be the portion of the helix parametrised r(t) = (sin(t), cos(t), t) between the points (0, –1, –7) and (0, –1, 7). Evaluate F. dr .
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