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Question Number 162521 by HongKing last updated on 30/Dec/21

$$\mathrm{For}\mathrm{every}\mathrm{positive}\mathrm{real}\mathrm{number}\mathbf{x},\mathrm{let}$$$$\mathrm{g}\left(\mathrm{x}\right)=\underset{\mathbf{r}\to 0}{\lim }{({(\mathrm{x}+1)}^{\mathbf{r}+1}-{\mathrm{x}}^{\mathbf{r}+1})}^{\frac{1}{\mathbf{r}}}$$$$\mathrm{Find}:\underset{\mathbf{x}\to \mathrm{\infty }}{\lim }\frac{\mathrm{g}\left(\mathrm{x}\right)}{\mathrm{x}}$$

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