Question Number 192646 by pascal889 last updated on 24/May/23
$$\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\Rightarrow\mathrm{3}} \sqrt{\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{\mathrm{x}}+\mathrm{3}}{\boldsymbol{\mathrm{x}}−\mathrm{3}}} \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{limit}} \\ $$
Answered by Subhi last updated on 24/May/23
$${lim}_{{x}\rightarrow\mathrm{3}} \sqrt{\frac{\left({x}−\mathrm{3}\right)\left({x}−\mathrm{1}\right)}{{x}−\mathrm{3}}} \\ $$$${lim}_{{x}\rightarrow\mathrm{3}} \sqrt{{x}−\mathrm{1}}\:=\:\sqrt{\mathrm{2}} \\ $$