Evaluate each limit. If the limit does not exist due to a vertical asymptote, then add an approach statement stating if
The denominator does not cancel out. That means that there will be a
in the denominator when we evaluate at , so the limit does not exist.
Graphically, there will be a vertical asymptote at
. That is why we are asked to find the limit from the right: we want to know if the graph approaches the asymptote towards or .
So evaluate a value that is to the right of
, and see if you get a positive or negative answer.
Therefore, from the right, the graph of
approaches the vertical asymptote towards .
This is a limit
. Think end behavior. Compare the highest power on the top and bottom. Be sure to consider their coefficients. (Careful!)
Think: The function is
. That is a horizontal line. All -values are .