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

• Recognize when a limit is indicating there is a vertical asymptote.
• Evaluate the limit as $x$ approaches a point where there is a vertical asymptote.
• Match graphs of functions with their equations based on vertical asymptotes.
• Discuss what it means for a limit to equal $\infty$.
• Define a vertical asymptote.
• Find horizontal asymptotes using limits.
• Produce a function with given asymptotic behavior.
• Recognize that a curve can cross a horizontal asymptote.
• Understand the relationship between limits and vertical asymptotes.
• Calculate the limit as $x$ approaches $\pm \infty$ of common functions algebraically.
• Find the limit as $x$ approaches $\pm \infty$ from a graph.
• Define a horizontal asymptote.
• Compute limits at infinity of famous functions.
• Find vertical asymptotes of famous functions.
• Identify horizontal asymptotes by looking at a graph.
• Identify vertical asymptotes by looking at a graph.