Question Number 184798 by Spillover last updated on 11/Jan/23
$${Show}\:{that}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}}{\mid{x}\mid}\:\:{does}\:{not}\:{exist} \\ $$
Commented by MJS_new last updated on 11/Jan/23
$${x}\rightarrow\mathrm{0}^{−} :\:\frac{{x}}{\mid{x}\mid}=\frac{{x}}{−{x}}=−\mathrm{1} \\ $$$${x}\rightarrow\mathrm{0}^{+} :\:\frac{{x}}{\mid{x}\mid}=\frac{{x}}{{x}}=+\mathrm{1} \\ $$