Asymptotes

Table of Contents

Vertical Asymptote

Existence

Find Via Limits

$ϵ$ : a number very close to 0.

Horizontal Asymptote

Existence

1. These occurs at the extremes of the function (i.e ${\lim }_{x\to \pm \infty }$)
2. Denominator degree $\le$ numerator degree

Find Via Limit

Finding Limits at Infinity

Slant Asymptotes

Existence

1. Cannot coexist with Horizontal Asymptotes
2. Denominator degree > Numerator degree

Find Via Long Division