We are so accustomed to seeing a single horizontal asymptote for the graph of a given function, but is it possible to have more than one? Duration: 9:25

On Example 8, let's use the graph of a piecewise function to evaluate a number of limits, some of which may or may not refer to horizontal, or perhaps vertical, asymptotes. Duration: 2:32

When direct substitution leads to the indeterminate form ∞/∞, we usually expect a horizontal asymptote, but is that always the case? To find out, just divide the top and the bottom of your function by the highest power of x in the denominator. Duration: 10:51

We often think of squares and square roots as direct inverses of each other, but as you may from your pre-calculus studies, it's not quite that simple. Duration: 6:18

Now that we have resolved the square-square-root-not-quite-inverse situation, let's apply it to some limits at infinity to find two horizontal asymptotes. Duration: 10:16

The limits at infinity in Examples 11, 12, and 13 refer to the end behavior of our graph with some possible oscillation thrown just to keep things indecisive. Duration: 7:08

In the conclusion of this lesson, we discuss relative growth rates as an aid to evaluate limits at infinity and reveal yet another indeterminate form: ∞−∞. Duration: 9:25