What is a limit?

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

Explain what is meant by a (two-sided) limit.
Use limits to help understand local behavior of functions.
Evaluate limits using a graph (or state that the limit does not exist).
Distinguish between limit values and function values.
Identify some conditions under which a limit will not exist.
Describe possible issues when estimating limits using tables.
Explain what is meant by a one-sided limit.
State the relationship between one-sided and two-sided limits.
Use one-sided limits to conclude whether a two-sided limit exists or not.

Skills you may want to brush up on first
To be ready to achieve these objectives, you may need to review the following trigonometry and algebra topics:

Functions (including function notation, interpreting graphs of functions, and identifying the domain/range of a function)