Determine the values of the following limits. If the limit does not exist, indicate why not.
This is a one-sided limit because the domain of
Consequently, the limit exists from the right, but not from the left.
Factor first. If you can 'cancel out' the denominator, then the graph has a hole (not a vertical asymptote) and the limit exists.
Evaluate. The denominator will not equal zero. So the limit and the actual value agree.
Both graphs have the same end behavior (horizontal asymptote).
For limits in which
or , we are looking for end behavior. For example, is there a horizontal asymptote?
Since the numerator has a higher power,
, than the denominator, , there is no horizontal asymptote. Thus the limit goes to either or .
The limit goes to
Refer to hint in part (e).