In our previous article, we introduced the concept of limits by rationalization, and worked through why it works.
To combine some aspects of limits we’ve already learned, let’s do some more problems, now using piecewise functions, and discuss the one piece of intuition about limits I have purposely been leaving out.
“Limits by Piecewise Functions” is actually kind of a misnomer, as it errs more on the side of an application of limits than it is a way to solve limits.
Nevertheless, it is a helpful tool to algebraically represent complex limits that cannot be defined with a single function.