Author: Tinku Tara

Question Number 69593 by ahmadshahhimat775@gmail.com last updated on 25/Sep/19 Commented by mathmax by abdo last updated on 25/Sep/19 $${let}\:{f}\left({x}\right)\:=\frac{\sqrt{\mathrm{6}−{x}}−\mathrm{2}}{\mathrm{3}−\sqrt{\mathrm{11}−{x}}}\:\Rightarrow \\ $$$${lim}_{{x}\rightarrow\mathrm{2}} \:{f}\left({x}\right)\:={lim}_{{x}\rightarrow\mathrm{2}} \:\:\:\:\:\frac{\left(\sqrt{\mathrm{6}−{x}}−\mathrm{2}\right)\left(\sqrt{\mathrm{6}−{x}}+\mathrm{2}\right)\left(\mathrm{3}+\sqrt{\mathrm{11}−{x}}\right)}{\left(\mathrm{3}−\sqrt{\mathrm{11}−{x}}\right)\left(\mathrm{3}+\sqrt{\mathrm{11}−{x}}\right)\left(\sqrt{\mathrm{6}−{x}}+\mathrm{2}\right)} \\ $$$$={lim}_{{x}\rightarrow\mathrm{2}}…