This demo opens with six windows.

The "Function Graph and Domain" window shows the domain of the function as a wireframe colored according to the value of the function there.  This window also shows the curve to be examined running through this domain with a dot to represent the function at t0, and the curve is highlighted with white for all values of t such that |t-t0| < delta.

The "Function Graph" window shows the same curve as the "Function Graph and Domain" window highlighted in the same way.  The domain has been removed, and a sphere has been added around the point (x(t0),y(t0),z(t0)).  This sphere has two colors on it representing a maximum and minimum value that the function can obtain to remain within an epsilon neighborhood of the function value at t0.  Thus if the white shaded portion of the curve lies within the sphere and the colors on this portion remain between the two colors on the sphere then this portion of the curve lies within an epsilon-neighborhood for the chosen epsilon.

Due to the difficulty of determining if the curve remains between two colors, four slice windows have been included.  Each one of these windows omits one variable.  Again the white shaded portion of the curve represents the portion of the curve for t such that |t-t0| < delta.  The pink spheres have radii epsilon/3.  Thus if all of the white curve portions in these slice windows lie within the pink spheres for any choice of epsilon, then the function is continuous at t0.