12.4: limits at infinity and limits of sequences

Limits of infinity: as the limit of f(x) as x approaches -infinity is L1. The limit of f(x) as x approaches infinity is L2.

Here are some rules regarding limits of infinity 

The limit of 1/x^r as x approaches infinity is 0. The limit leans towards the right 

The limit of 1/x^r as x approaches -infinity is 0. Limits leans towards left.

For rational functions... Say a^n/b^m 

If n<m, the limit is 0

If n=m the limit is a/b

If n> m, there is no limit

For example

An = 2n + 1/n+4.... 

N=m 

Limit = 2/1=2