AsymptoticGreater
AsymptoticGreater[f, g, x -> x*] gives conditions for f(x) ≻ g(x) or f(x) ∈ ω(g(x)) as x -> x*.
AsymptoticGreater[f, g, {x1, ..., xn} -> {x1*, ..., xn*}] gives conditions for the multivariate case.
Examples
Test if one function dominates another:
AsymptoticGreater[x^3, x^2, x -> Infinity]
(* True *)Please visit the official Wolfram Language Reference for more details.