Question

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

Use the squeeze theorem to find the answer.

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`.