Question Number 207382 by efronzo1 last updated on 13/May/24
Answered by sniper237 last updated on 13/May/24
$$\overset{{X}=^{\mathrm{3}} \sqrt{{x}−\mathrm{2}}} {=}\underset{{X}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{X}^{\mathrm{6}} +\mathrm{2}{X}^{\mathrm{3}} +{X}}{\:^{\mathrm{3}} \sqrt{\mathrm{4}−\mathrm{2}\sqrt{\mathrm{3}{X}^{\mathrm{3}} +\mathrm{4}}−{X}^{\mathrm{3}} \sqrt{\mathrm{3}{X}^{\mathrm{3}} +\mathrm{4}}}} \\ $$$$\:\:\:=\underset{{X}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{X}^{\mathrm{5}} +\mathrm{2}{X}^{\mathrm{2}} +\mathrm{1}}{\:^{\mathrm{3}} \sqrt{\frac{−\mathrm{12}}{\mathrm{4}+\mathrm{2}\sqrt{\mathrm{3}{X}^{\mathrm{3}} +\mathrm{4}}}−\sqrt{\mathrm{3}{X}^{\mathrm{3}} +\mathrm{4}}}} \\ $$$$=−\:^{\mathrm{3}} \sqrt{\frac{\mathrm{2}}{\mathrm{7}}}\: \\ $$