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. (a) Find the flux of F across the upward-oriented surface S,. (b) Show that F is incompressible and then use Gauss's Divergence Theorem to find the flux of F across the positively-oriented surface S. (c) Using items (a) and (b), find the flux of F across the upward-oriented surface S2.

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Q: 5. Use Divergence Theorem to find the outward flux of F(x,y, z) = (y²z)î + (2xy)ĵ + (z)k across the…

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A: There is no specific introduction for this question. Please go through the solution.

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