Using limits to detect asymptotes

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

Approximate a slant asymptote from the graph of a function. (§5.1)
Determine when a limit is indicating there is a vertical asymptote. (§5.2)
Evaluate the limit as $x$ approaches a point where there is a vertical asymptote. (§5.2)
Find vertical asymptotes of functions. (§5.2)
Find vertical asymptotes by looking at a graph. (§5.2)
Calculate horizontal asymptotes using limits.(§5.3)
Calculate the limit as $x$ approaches $\pm \infty$ of common functions algebraically. (§5.3)
Find the limit as $x$ approaches $\pm \infty$ from a graph. (§5.3)
Define a horizontal asymptote.(§5.3)
Compute limits at infinity of famous functions.(§5.3)
Identify horizontal asymptotes by looking at a graph.(§5.3)