Problem C: The surface S with parametrization |
r(u,v) = (u,v+u2,cos(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 (1,0,1) and the equation L(x,y,z) = g(1,0,1) of the level surface of the linearization of L. This will be identified later as the tangent plane at (1,0,1).
b) (2 points) Why are the vectors ru(u,v) and rv(u,v) tangent to S?
c) (4 points) Use b) to find the equation of the tangent plane at the point (1,0,1) again.