Answer the following: 1.) Determine the flux of F⃗ across the upward-oriented surface S1. 2.) Show that F⃗ is incompressible and then use Gauss’s Divergence Theorem to find the flux of F⃗ across the positively-oriented surface S. 3.) Using items (a) and (b), find the flux of F⃗ across the upward-oriented surface S2

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Answer the following:

1.) Determine the flux of F⃗ across the upward-oriented surface S1.
2.) Show that F⃗ is incompressible and then use Gauss’s Divergence Theorem to find the flux of F⃗ across the positively-oriented surface S.
3.) Using items (a) and (b), find the flux of F⃗ across the upward-oriented surface S2.

Let F(x,y,z)=(x-ye?,y+xe?,8–2z) and G be the solid below the paraboloid
z=4-x2-y? and above the xy-plane. Let S be the surface boundary of G,
and S, and S2 be the portions of S along the paraboloid and the xy-
plane, respectively.
Transcribed Image Text:Let F(x,y,z)=(x-ye?,y+xe?,8–2z) and G be the solid below the paraboloid z=4-x2-y? and above the xy-plane. Let S be the surface boundary of G, and S, and S2 be the portions of S along the paraboloid and the xy- plane, respectively.
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