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Question Number 184797 by Spillover last updated on 11/Jan/23
Show that   lim_(x→0) ((e^(1/x) −1)/(e^(1/x) +1))   does not exist
$${Show}\:{that}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\frac{\mathrm{1}}{{x}}} −\mathrm{1}}{{e}^{\frac{\mathrm{1}}{{x}}} +\mathrm{1}}\:\:\:{does}\:{not}\:{exist} \\ $$
Commented by MJS_new last updated on 11/Jan/23
let x=(1/t)  x→0^− : t→−∞ ⇒ lim=−1  x→0^+ : t→+∞ ⇒ lim=+1
$$\mathrm{let}\:{x}=\frac{\mathrm{1}}{{t}} \\ $$$${x}\rightarrow\mathrm{0}^{−} :\:{t}\rightarrow−\infty\:\Rightarrow\:\mathrm{lim}=−\mathrm{1} \\ $$$${x}\rightarrow\mathrm{0}^{+} :\:{t}\rightarrow+\infty\:\Rightarrow\:\mathrm{lim}=+\mathrm{1} \\ $$

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