Problem C: The surface S with parametrization r(u,v) = (cos(v) cos(u), cos(v) sin(u),v)is shown to the left. a) (4 points) Find an implicit equation g(x,y,z)=0 for this surface,
the linearization L(x,y,z) of g at the point P=(1/2,1/2,Pi/4)
and the equation L(x,y,z) = C
with constant C=g(1/2,1/2,Pi/4). This level surface
is the tangent plane at P. b) (2 points) Why are the vectors r_{u}(u,v) and r_{v}(u,v)
tangent to S at P? Compute them c) (4 points) Use b) to find the equation of the tangent plane at the
point P again. You should get the same plane as in a) |