hi guys, sorry to hastle everyone. I have a big assignment due tomorrow, and have had no luck at all with 2 of the questions. I really need solutions ASAP, and hate to ask, but im stuck and i am desperate for the solutions in order to pass the subject. If anybody can help me out, I will happily donate to this site quite generously!! (i must apologise if i am breaking any rules)

 

here they are:

 

1.

Verify the Gauss Divergence Theorem:

∫∫∫∇ ⋅F dxdydz= ∫∫ F .nˆ dA , where

 

the closed surface S is the sphere x^2 + y^2 + z^2 = 9 and the vector field

 

F = xz^2i + x^2 y j + y^2 z k .

 

2.

Consider a surface

S which is that portion of the plane 2x + 2y + z = 6

 

 

included in the first octant.

Evaluate the flux integral ∫∫ F nˆdA , where the vector field

 

F = [xy,−x^2 , x + z] and nˆ is a unit outer normal vector to S.

 

 

thanks in advance! i'm really desperate here...

We're pretty strict on not giving straight up answers to homework questions, so it'd help if you could tell us whereabouts you're stuck?

I went ahead and moved this to Homework Help to hopefully get quicker response if you reply back to the tree. And, yes, I completely concur with the tree that we will help you if you show us the work you've done up the point where you are stuck. Spoon feeding answers doesn't really help anybody, though, so it isn't done on this forum.