Problem 2 (2 points) Determine whether the following vector fields are conservative or not by ap- plying Clairaut's test. If they are conservative, find the potential function: 1. F(x,y) = xy'it xyj 2. F(x, y) = Va2 + y2 Vx2 + y2Problem 1 (2 points) Find the area of the portion of the surface given by 2.. 222 __3/2 +39 that lies above the region D of the mgr-plane given by D={(1r,-y):03352,0$y52I}. Problem 3 (2 points) For the following vector fields (a) F = -4yi + 5xj (b) F = 7yi + 3xj (c) F = 5yi - 5xj (d) F = 6yi - 4xj (e) F = -2yi + 3xj answer the following questions: 1. Which of the above vector fields is rotating the fastest in the counter-clockwise direction? 2. Which of the above vector fields is rotating the fastest in the clockwise direction? 3. Which one is not rotating at all