Question Number 160580 by LEKOUMA last updated on 02/Dec/21
$${Calculate}\: \\ $$$$\mathrm{1}.\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\frac{{x}\sqrt{\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)}}{\mathrm{1}+{e}^{{x}−\mathrm{3}} } \\ $$$$\mathrm{2}.\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{{x}^{\mathrm{3}} +\mathrm{5}}{{x}^{\mathrm{2}} +\mathrm{2}}\right)^{\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$