I need help to solve these problems please
MAT 240 Worksheet Chapter 16 Name 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)=(cosy+ycos x)i+(sin x-xsiny)J+yzk Calculate the divergence 2. 3. 4. of F at the point (0, 0, 1). LetF(x, y, z)=arcsin xi+xy2j+yz2k Find the curl(F). Let F(x,y)=(xy2_x2.)i+(ry+y2)/ Find the potential function of F. Determine which of the following vector fields is not conservative. a. b. (-2y' sin 2x)i +3y*(+cos 2x)j 5. Let C be the curve represented by rG) t(2-t)j, for 0sIs2. Find 3(x -y)ds Let F(x, y, z) = (2y-z)/ + (z-x)/ + (x-y)k an object moving along the straight line from the point (0, 0, 0) to the point (1, 1,0 Find the work done by the force F on 6. 7. Use the Fundamental Theorem of Line Integrals to evaluate 2xyzdt + x'zdy+ x'ydz where C is a smooth curve from (0,0,0) o(1,3,2) 8. Evaluate Jxyd+( dy where C is the square with vertices (0,0), (0, 1), (1, 0), and (1, 1) oriented counterclockwise.