### Home > APCALC > Chapter 2 > Lesson 2.3.2 > Problem 2-118

2-118.

Evaluate the following limits.

Factor the numerator.

Simplify.

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.

As

oscillates betweenand.

Asapproaches.

So this ratio has small values on the top and infinity on the bottom.