Question

lim_(x->oo) 4^x/(x!)

Use the squeeze theorem to find the answer.

Assuming, that x is integer.
Since 0<4^x/(x!)<4^x/5^x for x>11, and lim_(x->oo)0=lim_(x->oo)4^x/5^x=0, then, according to the squeeze theorem, lim_(x->oo)4^x/x=0.