Evaluate the following limits.
Factor the numerator.
A limit exists at a hole. What is the
-value of the hole?
Notice that this is a limit
. Compare the greatest powers of the numerator and denominator.
This is another limit
. Compare the terms with the highest powers in the numerator and denominator.
Think about the graph of
. It oscillates as . This means that it does not approaches a finite value AND does not approach . When a function oscillates, we say the limit does not exist.
Consider the numerator and the denominator separately.
oscillates between and .
So this ratio has small values on the top and infinity on the bottom.