
We explore functions that behave like horizontal lines as the input grows without bound.

Let’s start with an example:

Sometimes one must be careful, consider this example.

Note, since and we can also apply the Squeeze Theorem when taking limits at infinity. Here is an example of a limit at infinity that uses the Squeeze Theorem, and shows that functions can, in fact, cross their horizontal asymptotes.

It is a common misconception that a function cannot cross an asymptote. As the next example shows, a function can cross a horizontal asymptote, and in the example this occurs an infinite number of times!

We conclude with an infinite limit at infinity.