Evaluating a limit with exponential and factorials

Question

i'm having trouble with this question as i have tried multiple techniques and it didn't seem to lead me anywhere.

$\lim_{x \to \infty} \frac{10(x!)\; +\; 10^x }{x^{10}\;+\;x!}$

How would i go about solving this by hand?

Answer 1

x! is the most dominating term here. So divide numerator and denominator by x!.
And You will get $\frac{10}{1}$ = 10.