How do you find horizontal asymptotes using limits?
Evaluate the limits as
(If the limit fails to exist, then there is no horizontal asymptote on the right.)
(If the limit fails to exist, then there is no horizontal asymptote on the left.)
For rational functions, if one of the limits at infinity exists, then the other does as well and they are equal.
Other types of functions may have an asymptot on one side, but not the other -- e.g
or may have different left and right horizontal asymptotes -- e.g.