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Question Number 175994 by sciencestudent last updated on 10/Sep/22

lim_(x→∞) ((e^x −1)/x)=?

$${li}\underset{{x}\rightarrow\infty} {{m}}\frac{{e}^{{x}} −\mathrm{1}}{{x}}=? \\ $$

Answered by JDamian last updated on 10/Sep/22

∞

$$\infty \\ $$

Answered by cortano2 last updated on 11/Sep/22

=((e^∞ −1)/∞)=(∞/∞)=1

$$=\frac{{e}^{\infty} −\mathrm{1}}{\infty}=\frac{\infty}{\infty}=\mathrm{1} \\ $$

Commented by Ar Brandon last updated on 11/Sep/22

e^x ≫x as x→+∞  lim_(x→+∞) ((e^x −1)/x) → +∞

$${e}^{{x}} \gg{x}\:\mathrm{as}\:{x}\rightarrow+\infty \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\frac{{e}^{{x}} −\mathrm{1}}{{x}}\:\rightarrow\:+\infty \\ $$

Answered by Raxreedoroid last updated on 11/Sep/22

lim_(x→∞) ((e^x −1)/x)((∞/∞))  lim_(x→∞) (e^x /1)=+∞

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{e}^{{x}} −\mathrm{1}}{{x}}\left(\frac{\infty}{\infty}\right) \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{e}^{{x}} }{\mathrm{1}}=+\infty \\ $$

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