Section 1.5 - Limits at Infinity
Infinity is a slipery concept. We're going to take a narrow view of it where it just means, "something doesn't have an upper (or lower) bound". If we combine this with our Calculus-based limit concept we can make specific several ideas about asymptotes that you've probably talked about before in less technical terms.
Videos
Lectures
Sometimes, even when a limit doesn't exist, the function behaves in a way that's consistent enough that we want to be able to talk about it. For example, when a function is "unbounded" we're going to use "infinity" to describe its behavior. (lecture slides)
In Precalculus and College Algebra, horizontal asymptotes are defined in an experimental way, i.e. by finding points on the graph and looking for trends. By extending our definition of a limit to include "infinity" we can come up with a precise definition of this behavior. (lecture slides)
