Problem
given a function $f(x)$, defined on $[ \epsilon, \infty )$. Is there a way to "numerically estimate" whether the integral of the function diverges over the domain $[ \epsilon, \infty )$? i.e. Can I numerically estimate the left hand side of the equation and "estimate" that the left hand side goes to $\pm \infty$? $$\int_\epsilon^\infty f(x) dx = \left\lbrace \begin{array}{c} \infty \\ \text{or} \\-\infty \\ \text{or} \\ c \in \mathbb{R}\end{array}\right.$$
I don't know what, if any, numerical methods there are for doing something like this.