How are limits related to asymptotes?

1 Answer
Oct 19, 2014

Asymptotes are defined using limits.

Definition

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

lim_{x to a^-}f(x)=pminfty or lim_{x to a^+}f(x)=pminfty

Definition

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

lim_{x to +infty}f(x)=b or lim_{x to -infty}f(x)=b


I hope that this was helpful.