Question Number 104603 by john santu last updated on 22/Jul/20
$$\underset{{x}\rightarrow−\mathrm{2}} {\mathrm{lim}}\:{x}\mid{x}−\mathrm{2}\mid\: \\ $$
Answered by bobhans last updated on 22/Jul/20
$$\underset{{x}\rightarrow−\mathrm{2}^{−} } {\mathrm{lim}}{x}\mid{x}−\mathrm{2}\mid\:=\:\underset{{x}\rightarrow−\mathrm{2}^{−} } {\mathrm{lim}}{x}\left(−{x}+\mathrm{2}\right)=−\mathrm{8} \\ $$$$\underset{{x}\rightarrow−\mathrm{2}^{+} } {\mathrm{lim}}{x}\mid{x}−\mathrm{2}\mid\:=\:\underset{{x}\rightarrow−\mathrm{2}^{+} } {\mathrm{lim}}{x}\left(−{x}+\mathrm{2}\right)=−\mathrm{8} \\ $$