solve the answers handwritten but please type all the final answers together in the different section after solving. Thanks.

1. [-/1 Points] DETAILS SCALCET9 16.9.005. Use the divergence theorem to calculate the surface integral F . dS; that is, calculate the flux of F across S. F(x, y, z) = xyeli + xy-z'j - ye"k, S is the surface of the box bounded by the coordinate planes and the planes x = 9, y = 2, and z = 1 Need Help? Read It Watch It 2. [-/1 Points] DETAILS SCALCET9 16.9.007.MI. Use the divergence theorem to calculate the surface integral / / F . dS; that is, calculate the flux of F across S. F(x, y, z) = 3xy2i + xe?j + 2 k, S is the surface of the solid bounded by the cylinder y2 + z2 = 9 and the planes x = -1 and x = 1 Need Help? Read It Watch It Master It 3. [-/1 Points] DETAILS SCALCET9 16.9.009. Use the divergence theorem to calculate the surface integral F . ds; that is, calculate the flux of F across S. F(x, y z) = xei + (z - e))j - xyk, S is the ellipsoid x2 + 5y2 + 722 = 25 Need Help? Read It6. [-/1 Points] DETAILS SCALCET9 16.9.021.MI. A vector field F is shown. Use the interpretation of divergence derived in this section to determine whether the points P, and at P, are sources or sinks. X O div(F) is positive at both P, and P2. Therefore, P, and P, are both sources. O div(F) is positive at P, and negative at P2. Therefore, P, is a source and P, is a sink. O div(F) is negative at both P, and P2. Therefore, P, and P2 are both sinks. O div(F) is negative at P, and positive at P2. Therefore, P, is a sink and P2 is a source. Need Help? Read It Watch It Master ItT. [-11 Points] DETAILS SCALCETQ 16.9324. Plot the vector eld and guess where div(F} :> D and where divEF] D for y b x; div[F} e: I] for y e: X D div(F} :> D for y <: x:. div q: for y :> X D div{F} :> D for y 3' x; div[F) : I1] For 1! z x O div{F} :2 D for y <: x div z .3 for y :> x Calculate div(F) to check your guess. Need Help? 4. [-/1 Points] DETAILS SCALCET9 16.9.013. Use the divergence theorem to calculate the surface integral /[ F . dS; that is, calculate the flux of F across S. F(x, y z) = x2zi + x23j + y In(x + 1) k, S is the surface of the solid bounded by the planes x + 2z = 4, y = 6, x = 0 y = 0, and z = 0 x + 22 = 4 Need Help? Read It 5. [-/1 Points] DETAILS SCALCET9 16.9.017. Use the divergence theorem to calculate the surface integral / / F - as; that is, calculate the flux of F across S. F = [rlr, where r = xi + yj + zk, S consists of the hemisphere z = \\ 4 - x2 - y2 and the disk x2 + y? s 4 in the xy-plane Need Help? Read It