1Aasymplimits


 * Asymptotes as Limits **

We can discuss the behaviour of graphs near asymptotes using Limits notation.

Example

In this graph, we can see that as x → + ¥, y → 0 or math \begin{matrix} \lim \\ x \to \infty \end{matrix} \;\; y = 0 math

Also, we can see that as x → 2 from the positve end, y → + ¥ or math \begin{matrix} \lim \\ x \to 2^+ \end{matrix} \;\; y = \infty math

And as x → 2 from the negative end, y → – ¥ math \begin{matrix} \lim \\ x \to 2^- \end{matrix} \;\; y = -\infty math

.