Question

MAT 240 Quiz 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)=(x31nz)/4(xe-y)/-(y2+22k. Calculate the divergence of Fat the point (2, In2, 1). 2. Let F(x,y,z) - cos.xi+sinyj +e k. Calculate the curl F at the point (1, 1, 1). 3. Let Fox,y)-e'i+(xe+y)j. Find the potential function of F. 4. Determine if the following vector field is conservative. F(x, y, z)= (2xy +Z2)/+12/t (2xz + π cos k 5. Let C be the curve represented by r()j.for Ostsi. Find [Gx-2p)ds 6. Let F(x,y, z) = (2x-y)/ + 2zj + (y-z) Find the work done by the force F on an object moving along the straight line from the point (0, 0, 0) to the point (1, 1, 1). Use the Fundamental Theorem of Line Integrals to evaluate fc2cos2x cos2yi-2sin 2xsin 2y where C is a smooth curve from 0, to 7. 8. Evaluate e' siny dr + e' cosy dy where C is the square with vertices (0,0), (1, 1), (0, 2), and (-1, 1) oriented counterclockwise.