This demo shows the graph of x(u,v),y(u,v),z(u,v).

In the graph labeled u,v,x(u,v), there are two pink cones through a point (u0,v0,x(u0,v0)), one with a slope ε greater than that of the tangent plane and one with a slope ε less than that of the tangent plane, while in the graph labeled u,v,y(u,v), there are two cyan cones through a point (u0,v0,y(u0,v0)), one with a slope ε greater than that of the tangent plane and one with a slope ε less than that of the tangent plane, and finally in the graph labeled u,v,z(u,v), there are two magenta cones through a point (u0,v0,y(u0,v0)), one with a slope ε greater than that of the tangent plane and one with a slope ε less than that of the tangent plane.  If the curve is differentiable at (u0,v0), you should always be able to choose a δ small enough that the portion of the surfaces u,v,x(u,v), u,v,t(u,v), and u,v,z(u,v) in a disc of radius δ centered at (u0,v0) lies inside the pink, cyan, and magenta cones respectively.