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.