AsymptoticLess

AsymptoticLess[f,g,x->x*] gives conditions for f(x)≺g(x) or f(x)∈o(g(x)) as x->x*.

AsymptoticLess[f,g,{x1,…,xn}->{x1*,…,xn*}] gives conditions for f(x1,…,xn)≺g(x1,…,xn) or f(x1,…,xn)∈o(g(x1,…,xn)) as {x1,…,xn}->{x1*,…,xn*}.

Examples

Check if x grows slower than x^2 as x approaches infinity:

AsymptoticLess[x, x^2, x -> Infinity]
(* True *)

Compare growth rates:

AsymptoticLess[Log[x], x, x -> Infinity]
(* True *)

Please visit the official Wolfram Language Reference for more details.