Question

How are limits related to asymptotes?

Answer 1

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`

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I hope that this was helpful.