(937, #17) Find an equation of the tangent plane to the given parametric surface at the specified point.

Solution:

Compute the tangent vectors.

The cross product of these two will give us the normal.

At the point ( 0, 0, 0 ), the parametric equations are

Solving this system of equations gives us . The normal vector at point ( 0, 0, 0 ) is . Therefore, the tangent plane at point ( 0, 0, 0 ) is

by C.A.H.