## Mathematical Analysis## Calculus Basics |

## What are horizontal asymptotes in association with limits? |

A *horizontal asymptote* is similar to a vertical asymptote, but it is associated with the *y* axis. For example, for the function

gives a solution of:

and, thus, the implied limit is:

This is because we know that:

And as *x* gets larger (or closer to ±∞) the points on the graph come closer to the horizontal line *y =* 2 (seen as a dashed line on the graph on page 225), which is called the horizontal asymptote.