Question 1:

(1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) 21 X The side of S is given by x2 + 1 = 4, and its height is 4. (a) Give a parametric equation, r(t) for the rim, C. r (t) = , with (For this problem, enter your vector equation with angle-bracket notation: .) (b) If S is oriented outward and downward, find Is curl (-2yi + 2x] + 2zk) . dA =(1 point) Let F = (2z + 2x3) i+ (3y + 6z + 6 sin(13) ) j + (2x + 6y + 3ez3 ) k. (a) Find curl F. curl F = (b) What does your answer to part (a) tell you about , F . di where C is the circle (x - 10)2 + (y - 20)2 = 1 in the xy-plane, oriented clockwise? So F . di = (c) If C is any closed curve, what can you say about J F . di? So F . di = (d) Now let C be the half circle (x - 10)~ + (y - 20) = 1 in the xy-plane with y > 20, traversed from (11, 20) to (9, 20). Find J F . dr by using your result from (c) and considering C plus the line segment connecting the endpoints of C. So F . dr =