Limit of a Function Defined by a Limit

For every positive real number $x$, let $$g(x) = \lim_{r \to 0} ((x+1)^{r+1} - x^{r+1})^{\frac{1}{r}}$$Find the integer closes to $\displaystyle 10\cdot \lim_{x \to \infty} \frac{g(x)}{x}$.