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This animation illustrates two limit case studies:

- A function tends toward a limit at a point.
- 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).

- 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…