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
begins at . 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.
Visualize the graph of
. 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).