What is a limit?

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After completing this section, students should be able to do the following.

Consider values of a function at inputs approaching a given point.
Understand the concept of a limit.
Use limits to understand local behavior of functions.
Calculate limits from a graph (or state that the limit does not exist).
Understand possible issues when estimating limits using nearby values.
Define a one-sided limit.
Explain the relationship between one-sided and two-sided limits.
Distinguish between limit values and function values.
Identify when a limit does not exist.
Define continuity in terms of limits.
Use the continuity of famous functions (on their domains) when computing limits.