Limits involving infinity can be formally defined using a slight variation of the

Infinite Limit
For any arbitrarily small
Similarly, the limit of
For a rational function
- If the degree of
is greater than the degree of , then the limit is positive or negative infinity depending on the signs of the leading coefficients; - If the degree of
and are equal, the limit is the leading coefficient of divided by the leading coefficient of ; - If the degree of
is less than the degree of , the limit is .
If the limit at infinity exists, it represents a horizontal asymptote at