MTH 241 Final: Math 241 F08Finalexam
Document Summary
Math 241ww- final exam - december 12, 2008. You are per- mitted two index cards, each no larger than 3 5, with whatever you like written on them: (10 points) let f (x, y) = x2 + 2y2. Use stokes" theorem to evaluate: curl ~f ~n ds. S: (15 points) let c be the curve of intersection of the plane y + z = 7 and the cylinder x2 + y2 = 4, oriented to be counterclockwise when viewed from above. ~f d~r where f (x, y, z) = ( y2, x, z2): (15 points) let s be the cylinder (including top and bottom) x2 + y2 = 1, 0 z 1, with outward pointing normal. Let ~f (x, y, z) = (x3, y3, e z). ~f ~n ds: (10 points) let s be the portion of the paraboloid z = x2 + y2 which lies between the planes z = 1 and z = 4.
