Editing Limit of a function (section)

===Limits at infinity for rational functions===
[[File:Tamasol SVG.svg|thumb|300px|Horizontal asymptote about {{math|1=''y'' = 4}}]]
There are three basic rules for evaluating limits at infinity for a [[rational function]] <math>f(x) = \tfrac{p(x)}{q(x)}</math> (where {{mvar|p}} and {{mvar|q}} are polynomials):
*If the [[Degree of a polynomial|degree]] of {{mvar|p}} is greater than the degree of {{mvar|q}}, then the limit is positive or negative infinity depending on the signs of the leading coefficients;
*If the degree of {{mvar|p}} and {{mvar|q}} are equal, the limit is the leading coefficient of {{mvar|p}} divided by the leading coefficient of {{mvar|q}};
*If the degree of {{mvar|p}} is less than the degree of {{mvar|q}}, the limit is 0.

If the limit at infinity exists, it represents a horizontal asymptote at {{math|1=''y'' = ''L''}}. Polynomials do not have horizontal asymptotes; such asymptotes may however occur with rational functions.