MA 26100 Final: Spring 2008, Final
Document Summary
Spring 2008: let z = f(x, y) is di erentiable, and let x = s2 t, y = t3 ln(1 + s). Spring 2008: find the total ux of the vector eld. F = (3x, xy, 1) across the boundary of the box d = {|x| 1, |y| 2, |z| 3}: 144, 0, 72, 9, 27. 2 , 1 v 4 r(u, v) = (3 cos u, 3 sin u, v), 2 u r(u, v) = (3 sin u, 3 cos u, v), 0 u , 1 v 4 r(u, v) = (3 cos u, v, 3 sin u), 2 u r(u, v) = (3 sin u, v, 3 cos u), 2 , 1 v 4: the surface s is best represented para- metrically by. Spring 2008: let r be bounded by the curve y = 2 x2 and the line y = x, and let c be its boundary, positively oriented.
