# How are limits related to asymptotes?

Oct 19, 2014

Asymptotes are defined using limits.

Definition

A line $x = a$ is called a vertical asymptote of a function $f \left(x\right)$ if at least one of the following limits hold.

${\lim}_{x \to {a}^{-}} f \left(x\right) = \pm \infty$ or ${\lim}_{x \to {a}^{+}} f \left(x\right) = \pm \infty$

Definition

A line $y = b$ is called a horizontal asymptote of $f \left(x\right)$ if at least one of the following limits holds.

${\lim}_{x \to + \infty} f \left(x\right) = b$ or ${\lim}_{x \to - \infty} f \left(x\right) = b$

I hope that this was helpful.