Limits at Infinity
Newsflash: when taking limits we don't have let x approach some fixed number. We can also see what happens as x blows up to ±∞.
We write these limits as
These limits look at where the function f(x) is attempting to reach as x moves further and further along the number line. If the limit exists, we say that the limit is a horizontal asymptote of f. Before we go into more depth with the function side of things, we'll look at some silly examples.