Suppose F(x, y, z) = (x, y, 52). Let W be the solid bounded by the paraboloid z = x² + y² and the plane z = 25. Let S be the closed boundary of W oriented outward. (a) Use the divergence theorem to find the flux of through S. SS F.dà = S (b) Find the flux of F out the bottom of S (the truncated paraboloid) and the top of S (the disk). Flux out the bottom= Flux out the top =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Suppose F(x, y, z) = (x, y, 5z). Let W be the solid
bounded by the paraboloid z = x² + y² and the plane
25. Let S be the closed boundary of W oriented
outward.
(a) Use the divergence theorem to find the flux of
through S.
ff ² · dä
=
-0
S
(b) Find the flux of Fout the bottom of S (the truncated
paraboloid) and the top of S (the disk).
Flux out the bottom=
Flux out the top =
Transcribed Image Text:Suppose F(x, y, z) = (x, y, 5z). Let W be the solid bounded by the paraboloid z = x² + y² and the plane 25. Let S be the closed boundary of W oriented outward. (a) Use the divergence theorem to find the flux of through S. ff ² · dä = -0 S (b) Find the flux of Fout the bottom of S (the truncated paraboloid) and the top of S (the disk). Flux out the bottom= Flux out the top =
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