AsymptoticEquivalent

AsymptoticEquivalent[f,g,x->x*] gives conditions for f(x)∼g(x) as x->x*.

AsymptoticEquivalent[f,g,{x1,…,xn}->{x1*,…,xn*}] gives conditions for f(x1,…,xn) ~g(x1,…,xn) as {x1,…,xn}->{x1*,…,xn*}.

Please visit the official Wolfram Language Reference for more details and examples on core symbols.