1. a) prove gauss law for the feild of a single point charge r^2= x^2+y^2+z^2
b) how would you extend this proof to cover the case of an arbitrary charge distribution?
2. derive the unit normal vector for surfaces given by y=g(x,z_ x=h(y,z)
3. find the moment of inertia about the z axis of the hemispherical shell of z= (2^2-x^2-y^2)^(1/2)