### Home > CALC > Chapter Ch2 > Lesson 2.3.2 > Problem 2-118

2-118.

Evaluate the following limits. Homework Help ✎

Factor the numerator.

Simplify.

A limit exists at a hole. What is the *y*-value of the hole?

Notice that this is a limit *x*→∞. Compare the greatest powers of the numerator and denominator.

This is another limit *x*→∞. Compare the terms with the highest powers in the numerator and denominator.

Think about the graph of *y* = sin*x*. It oscillates as *x*→∞. 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 *x*→∞, *y* = sin*x* oscillates between *y* = −1 and *y* = 1.

As *x*→∞, *y* = *x* approaches ∞.

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