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Question-210918




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

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