# Boundary at a pointHTML5

## Summary

This animation illustrates two limit case studies:

1. A function tends toward a limit at a point.
2. A function does not have a limit at a point.

Click and then slide the horizontal lines (tab 1) or the vertical lines (tab 2).

## Learning goals

• To understand the concept of limits defined and undefined at a point.

Let f be a function defined on the subset of real numbers. a is a value in the range of f.

f has a finite limit ℓ as x approaches a, means that there is a real ε and a real α such that the…