
Home > CALC > Chapter 3 > Lesson 3.2.1 > Problem 3-51
3-51.
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 −∞
Evaluate.
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.