1. Prove that the divergence of a curl is always zero. Check this for the function

2. Check Stokes'theorem for the function in Problem 1 using the triangle in the y-z plane with verticies (0,0,0), (0,1,0), and (0,0,2).

3. Check the divergence theorm for the function

For the volume use a hemisphere of radius R resting on the x-y plane and centered at the origin.