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lim-x-xE-x-3-x-2-sin-x-




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

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