Problem B: 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 gradient of g and the equation ax+by+cz=d of the tangent plane at the point (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.