Limit Involving Factorials

Question

How would you go about calculating

$$ \lim_{x \to \infty} \frac{x!}{(x - k)!} $$

for some constant $k > 0$?

Answer 1

Hint: $\frac{x!}{(x-k)!} = (x-k+1)*(x-k+2)*...*(x-1)*x$

Answer 2

Take upper and lower bounds: $$ (x-k+1)^k \leq x(x-1) \ldots (x-k+1) \leq x^k $$
and apply squeeze lemma. What do you get?