APPM 2350 Final: appm2350summer2016examfinal_sol
Document Summary
Summer 2016: (16 pts) let f = h3x + cos y, 2y + sin z, ex + 5zi. Find the outward ux of f through the surface enclosing the region inside x2 + z = 1, above the xy-plane and between y = 0 and y = 2. The surface s and the region w it encloses satisfy the hypotheses of gauss" (divergence) theorem with. 0 (cid:0)1 x2(cid:1) dy dx: (10 pts) find the area under the graph of z = 100(x2 + 2y2) lying above the second quadrant portion of the circle of (cid:4) radius 2. The area is given byz with /2 t . Then r (t) = 2 sin t i + 2 cos t j and kr (t)k = 2. Thus f (x, y) ds where f (x, y) = 100(x2+2y2) and c can be parameterized by r(t) = 2 cos t i+2 sin t j. /2(cid:0)1 + sin2 t(cid:1) dt = 800z .
