Question Number 88985 by jagoll last updated on 14/Apr/20
$$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\mathrm{ln}\:\mid{x}−\mathrm{3}\mid\: \\ $$$${exist}\:{or}\:{no}? \\ $$
Commented by mr W last updated on 14/Apr/20
$${no}. \\ $$
Commented by jagoll last updated on 14/Apr/20
$${because}\: \\ $$$$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\mathrm{ln}\:\mid{x}−\mathrm{3}\mid\:=\:−\infty\:{sir} \\ $$
Commented by mr W last updated on 14/Apr/20
$${yes} \\ $$
Commented by mr W last updated on 15/Apr/20
$$−\infty\:{or}\:+\infty\:{is}\:{not}\:{a}\:{value}!\:{when}\:{you} \\ $$$${write}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}{f}\left({x}\right)=\infty,\:{it}\:{means}\:{in}\:{daily} \\ $$$${language}\:{that}\:{there}\:{is}\:{no}\:{limit}.\:\:{because} \\ $$$${the}\:{function}\:{can}'{t}\:{go}\:{close}\:{to}\:{a}\:{value}. \\ $$$$ \\ $$$${this}\:{is}\:{the}\:{same}\:{as}\:{when}\:{you}\:{say}\:{that} \\ $$$${you}\:{still}\:{have}\:{money}\:{even}\:{when}\:{the} \\ $$$${numver}\:{of}\:{money}\:{you}\:{have}\:{is}\:{zero}. \\ $$
Commented by mr W last updated on 15/Apr/20
Commented by mr W last updated on 15/Apr/20
$${this}\:{is}\:{for}\:{the}\:{first}\:{day}\:{when}\:{lerning} \\ $$$${about}\:{limit}. \\ $$
Commented by malwaan last updated on 15/Apr/20
$$\underset{\boldsymbol{{x}}\rightarrow\mathrm{3}^{+} } {\boldsymbol{{lim}}}\:\boldsymbol{{ln}}\mid\boldsymbol{{x}}−\mathrm{3}\mid\:=\:−\infty \\ $$$$\underset{\boldsymbol{{x}}\rightarrow\mathrm{3}^{−} } {\boldsymbol{{lim}}}\:\boldsymbol{{ln}}\mid\boldsymbol{{x}}−\mathrm{3}\mid\:=\:−\infty \\ $$$$\Rightarrow\:\underset{\boldsymbol{{x}}\rightarrow\mathrm{3}} {\boldsymbol{{lim}}}\:\boldsymbol{{ln}}\mid\boldsymbol{{x}}−\mathrm{3}\mid\:=\:−\infty \\ $$$$\left({so}\:{limit}\:{exist}\right){or}\:{no}\:??? \\ $$
Commented by john santu last updated on 15/Apr/20
$${yes}.\:{i}\:{agree}. \\ $$$$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\mathrm{ln}\:\mid{x}−\mathrm{3}\mid\:\Rightarrow{exist}\: \\ $$
Commented by jagoll last updated on 15/Apr/20
$${i}\:{also}\:{think}\:{like}\:{that}. \\ $$$${by}\:{definition}\:{if}\: \\ $$$$\underset{{x}\rightarrow{a}^{+} } {\mathrm{lim}}\:{f}\left({x}\right)\:=\:\underset{{x}\rightarrow{a}^{−} } {\mathrm{lim}}\:{f}\left({x}\right)\: \\ $$$${then}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:{f}\left({x}\right)\:{exist}\: \\ $$