1. Find the critical points of the given function and determine whether they are local maxima, local minima, or saddle points f (x, y) = In(2 + sinxy).3. Evaluate J'H dxdydz where W is the solid bounded by the spheres x2 + y? + 22 = a2 and x2 + 3:2 + 22 = b2; where a > b > D. (Hint: A change of coordinates would be useful]. \f6. Let F(x.y,z) = (3.313. 0). A hot-air balloon has the truncated spherical shape shown in the gure. The hot gases escape through the porous envelope with a velocity vector eld V(x,y,z) = VxF. In the diagram R = 5. We compute the volume ow rate of the gases through the surface. [a] The ux is given by the surface integral J5] (er) -dS. We use Stoke's Theorem to evaluate this integral. Stoke's Theorem gives the flux as the line integral, ood?) -ds = I F-ds, s c Where C is the boundary of the surface. The boundary of our surface is the circle at the bottom of the balloon. Parameterize the circle