- 3 Let F X Y Z 0 0 X And Let S Be The Portion Of The Paraboloid Z 1 X Y Above And Including The X Y Plane W 1 (64.71 KiB) Viewed 128 times
3. Let F(x, y, z) = (0, 0, x) and let S be the portion of the paraboloid z=1-x² - y² above and including the x-y plane with normal n pointing upwards (i.e. non- negative z-coordinate).. (a) Find a parametrisation of the surface S with normal n pointing upwards. (b) Use the parametrisation from part (3a) to calculate 11. F (F.n) ds. (c) Find a parametrisation of the boundary of S. Hint: show that the boundary of S is the circle x² + y² = (F. (d) Use Stokes' theorem and the parametrisation for part (3c) to calculate n) ds. 2TT Given: curl(0,²,0) = (0, 0, x) and cos³0 de = 0. 10 Past papers May 2019 C