• Evaluate the surface integral s F dS where F= (3x, z,-y) and S is the part of the sphere x² + y²+z² = 9 in the first octant, with orientation toward the origin. A parametrization for S is 7(u, v) = (3 sin v cos u, 3 sin v sin u, 3 cos v) over the domain [0, 1] × [0, 1]. JJs F- ds =

Find both parametric and rectangular representations for the plane tangent to r(u,v)=u2i+ucos(v)j+usin(v)kr(u,v)=u2i+ucos⁡(v)j+usin⁡(v)k at the point P(4,−2,0)P(4,−2,0).One possible parametric representation has the form⟨4−4u⟨4−4u ,  , 4v⟩4v⟩(Note that parametric representations are not unique. If your first and third components look different than the ones presented here, you will need to adjust your parameters so that they do match, and then the other components should match the ones expected here as well.)The equation for this plane in rectangular coordinates has the form x+x+  y+y+  z+z+  =0

Determine the area of the parametric surface S with equation Ŕ(u, v) = (u²+v², 2uv, u²—v²), where 0 ≤ ≤ 1 and 0 ≤ u ≤ 1. V