limx→∞ xnex=0,(n integer), for

If n is a negative integer, then n=-m, where m∈N.∴limx→∞ xnex=limx→∞ x−mex=limx→∞ 1xmex=0If n=0, thenIf n∈N, then,limx→∞ xnex=limx→∞ n!ex=0     [By L' Hospital's Rule]Hence, limx→∞ xnex=0 for all values of n.