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