Problem A: r(u,v) = (u,v2 + sin(u),cos(u)+v2) is a parametrized surface S. a) 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 (0,1,2). b) Why are the vectors ru(u,v) and rv(u,v) tangent to S? c) Use b) to find the equation of the tangent plane at the point (0,1,2) again.

Questions and comments to knill@math.harvard.edu

Math21b | Math 21a | Fall 2007 | Department of Mathematics | Faculty of Art and Sciences | Harvard University