Infinite Limits and Asymptotes
Read this section to learn how to use and apply infinite limits to asymptotes. Work through practice problems 1-8.
Horizontal Asymptotes
The limits of , as " " and " ," give us information about horizontal asymptotes of .
Example 6: Find any horizontal asymptotes of .
Solution: so the line is a horizontal asymptote of . The limit, as " , " is also so is the only horizontal asymptote of . The graphs of and are given in Fig. 7. A function may or may not cross its asymptote.
Fig. 7