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.