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Let p(x, y, z) = (x +2)y+xz². (a) Compute the vector field F = Vy. (b) Compute Jo F dr, where C is the piecewise-linear path starting at (0, 1, 1), traveling C straight to (2,-1, 3), and terminating at (-1,3,0). (c) Compute the circulation of F around the tilted ellipse parametrized by r(t)= (cost, 2 sint, cost), 0 ≤t≤ 2π.

Let p(x, y, z) = (x +2)y+xz². (a) Compute the vector field F = Vy. (b) Compute Jo F dr, where C is the piecewise-linear path starting at (0, 1, 1), traveling C straight to (2,-1, 3), and terminating at (-1,3,0). (c) Compute the circulation of F around the tilted ellipse parametrized by r(t)= (cost, 2 sint, cost), 0 ≤t≤ 2π.

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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10. Let y(x, y, z) = (x+2)y+xz². (a) Compute the vector field F = Vy. (b) Compute [F F. dr, where C is the piecewise-linear path starting at (0,1,1), traveling straight to (2,-1, 3), and terminating at (-1,3,0). (c) Compute the circulation of around the tilted ellipse parametrized by r(t)= (cost, 2 sint, cost), 0≤t ≤ 2π. (d) Compute the divergence VF and the curl V × F.
Transcribed Image Text:10. Let y(x, y, z) = (x+2)y+xz². (a) Compute the vector field F = Vy. (b) Compute [F F. dr, where C is the piecewise-linear path starting at (0,1,1), traveling straight to (2,-1, 3), and terminating at (-1,3,0). (c) Compute the circulation of around the tilted ellipse parametrized by r(t)= (cost, 2 sint, cost), 0≤t ≤ 2π. (d) Compute the divergence VF and the curl V × F.
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