Evaluate each limit. If the limit does not exist due to a vertical asymptote, then add an approach statement stating if y is approaching negative or positive infinity.
This limit can be evaluated without any fancy Algebra steps.
Refer to the hint in part (a). Limits like these suggest that the actual value
and the limit agree.
Factor first. Since the denominator
, we are investigating whether there is a hole or an asymptote.
.Compare the highest-power term in the numerator and denominator. Does the graph have a horizontal asymptote or does it approach or ?
Use the limits above to describe the shape of the graph of
. State all horizontal asymptotes, vertical asymptotes, and holes.
Refer to the Hints in parts (c) and (d).