Please help with 4-8

Complete the following on a separate sheet(s) of paper. Organize your work neatly and clearly mark your solutions. 1. Let F(x, y, z) = (e* sin y)i -(e* cos y) j + zk. Calculate the divergence of F at the point (In 2, ~ , 1) . 6 2. Let F(x, y, z) = x2i+ yj+z2k. Calculate the curl F at the point (1, 1, 1). 3. Let F(x, y) = sin yi + xcos yj. Find the potential function of F. f ( x , y ) = * sing + c 4. Determine if the following vector field is conservative. y X F (x, y )= Vit xy 1 + xy 5. Let C be the curve represented by r(t) = 4ti + 3tj, for Ots1. Find [ xyds 6. Let F(x, y) = (x- y)i+(x+y)j. Find the work done by the force F on an object moving along the curve C: 4costi + 3 sintj, Osts2x. 7. Use the Fundamental Theorem of Line Integrals to evaluate | 2xydx + (x2 + >?) dy where C is a smooth curve from (5, 0) to (0, 4). 8. Evaluate | cos ydx + (xy - x sin y) dy where C is the boundary of the region lying between the graphs of y = x and y = Vx