Programs like Mathematica or Wolfram Alpha are able to calculate very complex limits with apparent ease. I'm trying to make my own program to compute limits. I've searched all over, but haven't found anything about how they do it. What algorithm can I use to compute limits?
Unfortunately, there is no rigourous answer. They "cheat" by simply doing some basic reduction, and then looking up in a large database of general forms.
A generalized algorithm is undecidable, due to being equivalent to the zero-recognition problem.