1. Let Fyi-xj and C be the boundary of S, the part of the surface z = 4-2-y above the ry-plane, oriented upward. Calculate the circulation F.dr in two ways, directly and using Stokes' Theorem. 2. Use Stokes' Theorem to calculate F dr where = x+ y+ zk and C is the unit circle in the xz-plane, oriented counterclockwise when viewed from the positive y-axis. 3. If curl = (x+z)+5k, find fo F.dr, where C is a circle of radius 3, centered at the origin, where: (a) C is in the xy-plane, oriented counterclockwise when viewed from above. (b) C is in the xz-plane, oriented counterclockwise when viewed from the positive y-axis. = 4. Let Fy+x+zk. Find fc F.dr where C is the circle of radius 2 in the plane r+y+z=3, centered at (1, 1, 1) and oriented clockwise when viewed from the origin. 5. Let (zy) + (x z)] + (y x) k. Find f.dr where C is the circle of radius 2 in the plane x + y + z = 3, centered at (1, 1, 1) and oriented clockwise when viewed from the origin. 6. Evaluate the circulation of G = xyi+z3+3yk around a square of side 6, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. = 7. Find the flux of curl ((2 + cos(22)) 7+ (x + sin(y)) + y sin(x)) through the upper half of the sphere of radius 2 with center at the origin and oriented upward.