9. Let f(x, y, z) = xyze"y. (a) Compute the gradient vector field F = Vf (b) Let C be the curve obtained by intersecting the unit sphere x? + y? + z² = 1 with the plane x = including possible orientations for C and S; state Stokes' theorem for this region. %3D 1/2 and let S be the portion of the sphere with x > 1/2. Draw a figure (c) With F as in (a) and S as in (b), let G = F +(z – y)i + yk, and evaluate the surface integral (V × G) · dS.
9. Let f(x, y, z) = xyze"y. (a) Compute the gradient vector field F = Vf (b) Let C be the curve obtained by intersecting the unit sphere x? + y? + z² = 1 with the plane x = including possible orientations for C and S; state Stokes' theorem for this region. %3D 1/2 and let S be the portion of the sphere with x > 1/2. Draw a figure (c) With F as in (a) and S as in (b), let G = F +(z – y)i + yk, and evaluate the surface integral (V × G) · dS.
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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Transcribed Image Text:9. Let f(x, y, z) = xyze"y.
(a) Compute the gradient vector field F = Vf
(b) Let C be the curve obtained by intersecting the unit sphere x? + y? + z² = 1 with the
plane x =
including possible orientations for C and S; state Stokes' theorem for this region.
%3D
1/2 and let S be the portion of the sphere with x > 1/2. Draw a figure
(c) With F as in (a) and S as in (b), let G = F +(z – y)i + yk, and evaluate the surface
integral
(V × G) · dS.
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