Introduction: What is a limit?

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

Differentiate between how a limit acts approaching a point, and a function’s value at a point (§1.1, §1.2, §1.7 (P2))
Consider values of a function at inputs approaching a given point. (§1.1, §1.2, §1.4 (P1))
Recognize that using nearby points can’t ever grant certainty about the value of a limit. (§1.1, §1.5, §1.7 (P2))
Determine what kinds of applications are appropriate for a limit. (§1.2)
Compute limits using a graph (§1.3, §1.4 (P1))
Compute one-sided limits using a graph (§1.3, §1.4 (P1))
Determine when a limit fails to exist using a graph. (§1.3, §1.4 (P1))
Use One-sided limits to determine if a limit exists. (§1.5, §1.6)
Use Tables to get determine if a limit is likely to exist or not. (§1.5), §1.7 (P2)
Correctly interpret and utilize the notation for limits, including one-sided limits. (§1.6)
Determine when a limit fails to exist by knowing information about left and right limit values (without graphs). (§1.6)