Please help me with these 3 questions

2. Let S = {(x, y, z) : x2 + y? + (1 -2)2 = 2 and z 2 0}, with inward-pointing [10pts] normals, and with oriented boundary OS. Let F(x, y, z) = (x + z,23 - ey, z). (a) Sketch S and OS and indicate the orientation of OS. (b) Verify Stokes Theorem for S and F. Hint: Use Question 1. 3. Let F : R3 - R3 be defined by [5pts] F(x, y, z) := ((1 + xy)ery + 2, x2ery, 2xz) Is the vector field equal to the gradient of a function? Why or why not? If it is, define a function f : R3 - R such that Vf = F.4. Define oriented surfaces: D := {(x, y, 0) : x2 + y?