Math 21a, Fall 2008
Week 6 Problems B, Math 21a, Multivariable Calculus
A Tangent Plane Problem
Course head: Oliver Knill
Office: SciCtr 434
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.

Questions and comments to
Math21b | Math 21a | Fall 2008 | Department of Mathematics | Faculty of Art and Sciences | Harvard University