Question Number 200864 by Rydel last updated on 25/Nov/23
$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\frac{{xE}\left({x}\right)+\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{sin}\:{x}}} \\ $$
Answered by Mathspace last updated on 25/Nov/23
$$={lim}_{{x}\rightarrow+\infty} \frac{{xE}\left({x}\right)+\mathrm{3}}{{x}\sqrt{\mathrm{1}+\frac{{sinx}}{{x}^{\mathrm{2}} }}} \\ $$$$={lim}_{{x}\rightarrow+\infty} \frac{{E}\left({x}\right)+\frac{\mathrm{3}}{{x}}}{\:\sqrt{\mathrm{1}+\frac{{sinx}}{{x}^{\mathrm{2}} }}} \\ $$$$={lim}_{{x}\rightarrow+\infty} {E}\left({x}\right)=+\infty \\ $$