I informally introduce limits in geometry using inscribed and circumscribed polygons to bound the area and perimeter of a circle and also in area and perimeter of fractals strictly from a numeric viewpoint.
In pre-calc, we investigate bounding behavior of functions to a particular tolerance along with behaviour at points of discontinuity and approaching infinity.
We also talk about Zeno's paradox and infinite geometric sequences.
All of these instances are treated from an intuitive point of view and verified numerically.(limited to the capability of the calculator)
Tom Perschbacher American Embassy School New Delhi India