This demo shows a torus defined in 3-space by the parameterization:

* Torus=((2+cos(t))cos(s),(2+cos(t))sin(s),sin(t)) *

By taking this parameterizaaton, we use calculus to compute the tangent vectors, and thus we may parameterize the tangent plane.

This demo shows a surface graph in 3 space (and a portion of its tangent plane at (x,y)= (0,0)) of:

* z=cos(x)*cos(y)*

** Show wavy surface
and tangent plane**

This demo shows a saddle surface with a tangent plane at the origin. Notice that the Tangent Plane intersects the surface. The surface is given by:

*z=xy*

Click **here** to see the full
version of our lab, designed for use by UMTYMP Calculus III students.

By Andrew Youn, Samir Murty, and Charlie McGarraugh