Evaluate each limit. If the limit does not exist, say so but also state if y is approaching positive or negative infinity. Homework Help ✎
The denominator does not cancel out. That means that there will be a 0 in the denominator when we evaluate at x = −3, so the limit does not exist.
Graphically, there will be a vertical asymptote at x = −3. 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 −3, 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.
Think: The function is y = π. That is a horizontal line. All y-values are π.