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 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 .
- 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 approaches of common functions algebraically.
- Find the limit as approaches from a graph.
- Define a horizontal asymptote. function.
- 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.