Question Number 210918 by VICHET last updated on 22/Aug/24
Answered by Frix last updated on 22/Aug/24
$$\mathrm{Let}\:{x}={t}+\mathrm{11} \\ $$$$\underset{{t}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\frac{\mid{x}\mid}{{x}}\:=\underset{{t}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\frac{−{x}}{{x}}\:=−\mathrm{1} \\ $$$$\underset{{t}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mid{x}\mid}{{x}}\:=\underset{{t}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{{x}}{{x}}\:=\mathrm{1} \\ $$$$\Rightarrow\:\mathrm{Limit}\:\mathrm{does}\:\mathrm{not}\:\mathrm{exist} \\ $$