I'm trying to study limits for my calculus class, but my textbook doesn't seem to be making much sense. In one of the examples, it shows us how to prove that $\lim_{x\to3} x^2 = 9$, with the following:
$|x^2-9| < \epsilon\text{ if }0<|x-3|<\delta$ $|x+3||x-3| < \epsilon \text{ if }0<|x-3|<\delta$ Assume $\delta\le1$, which then gives $-1
I sort of get the above step, because that gives us a "boundary range" on either side of the limit that we're approaching. (Is that right?) However, the next step completely confuses me. The book draws the conclusion $5