3. Let F(x, y, z) ellipsoid x? (0, 2xz? cos(x2), 4.x(x2 + y?) 2ye+y), and...

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3. Let F(x, y, z) ellipsoid x? (0, –2xz? cos(x2), 4.x(x2 + y?) – 2ye+y"), and let S be the top half of the + y? + 4z2 = 1, oriented upward. %3D (a) Verify that div(F) = 0. %3D (b) Check that F curl(G), where G = (e+u", (22 + y²)², z² sin(x²)). , (2² + y²)², z² sin(r²)). 1 (c) Use Stokes' Theorem to evaluate the flux integral F. dS by considering a line integral of G along the boundary of S (don't forget orientation!). Note: This integral would be very hard if we only considered changing surfaces. 3. Let F(x, y, z) ellipsoid x? (0, –2xz? cos(x2), 4.x(x2 + y?) – 2ye+y"), and let S be the top half of the + y? + 4z2 = 1, oriented upward. %3D (a) Verify that div(F) = 0. %3D (b) Check that F curl(G), where G = (e+u", (22 + y²)², z² sin(x²)). , (2² + y²)², z² sin(r²)). 1 (c) Use Stokes' Theorem to evaluate the flux integral F. dS by considering a line integral of G along the boundary of S (don't forget orientation!). Note: This integral would be very hard if we only considered changing surfaces.

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