# Mathematica’s algorithm for limits of multivariable functions

What algorithm does Mathematica use to compute limits for functions in $\mathbb{R}^n$ with $n\geq2$? Here I refer to limits that present indeterminate forms. How can it test every possible path? Does it test a couple and then if they are all equal use epsilon-delta proof? If so, how would this work for Mathematica? Does it do it numerically?

• (1) It is a melange of methods, a poly-algorithm at her Polly finest. Feb 27 '18 at 22:36
• (2) For rational functions, and frequently for more general meromorphic functions, there are ways to reduce to a finite set of paths. It uses some heuristics to decide when one or another tactic might be more efficient. Feb 27 '18 at 22:38