6760, Math 21a, Fall 2009

Week 5 Problems C, Math 21a, Multivariable Calculus

A Tangent Plane Problem

Course head: Oliver Knill

Office: SciCtr 434

Email: knill@math.harvard.edu

Problem C: The surface S with parametrization r(u,v) = (u,v+uis 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 r_{u}(u,v) and r_{v}(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 knill@math.harvard.edu

Math21b | Math 21a | Fall 2009 |
Department of Mathematics |
Faculty of Art and Sciences |
Harvard University