| 3 | 4
Given a positive ε we can form the ε
interval about z0 = (0,0,f(x(t0),y(t0)) on the z-axis, and show
the two planes at levels z0 ± ε.
We can then find
ρ such that the graph of f(x,y) over the disc of radius ρ
centered at (x(t0),y(t0),0) will lie between the two horizontal planes.
Finally, we can find a &delta so small that if | t - t0 | < &delta,
then the image of the parametrics curve (x(t),y(t)) will lie inside the
disc of radius ρ and the curve (0,0,f(x(t),y(t))) will lie between
two horizontal planes.
The value of t0 is chosen on a slider bar, as well as
the position of the &delta interval. The value of ρ is chosen so
that the portion of the graph above the disc is between the planes, and
then &delta is chosen so that the image of the parametric curve lies in
the disc of radius ρ.