# How does the vertical asymptotes affect limits at infinity?

Mar 13, 2015

Vertical asymptotes and limits at infinity do not affect each other.

Being a bit careless (but clearer to many than being too careful):
,A vertical asymptote occurs at $a$ if $a$ is a finite value for $x$ that makes $y$ become $\infty$ or $- \infty$.

When we ask about the limit at infinity, we are asking if there is a finite values $b$ that $y$ approaches as x becomes $\infty$ or $- \infty$.

The roles of $x$ and $y$ are reversed. Which one are we 'trying to make infinite'?

Be careful to distinguish the phrases "infinite limit" ($y \rightarrow \pm \infty$)
as opposed to "limit at infinity ($x \rightarrow \pm \infty$).

Here are 2 links. (I haven't yet learned to embed them nicely.)