Question Number 58948 by Mikael_Marshall last updated on 01/May/19
$$\underset{{x}\rightarrow+\infty} {{lim}}\:\frac{\sqrt{{x}}}{\:\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}} \\ $$
Commented by maxmathsup by imad last updated on 01/May/19
$$={lim}_{{x}\rightarrow+\infty} \:\:\:\:\frac{\sqrt{{x}}}{\:\sqrt{{x}}\sqrt{\mathrm{1}+\sqrt{\frac{{x}+\sqrt{{x}}}{{x}^{\mathrm{2}} }}}}\:={lim}_{{x}\rightarrow+} \:\:\:\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\sqrt{\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{x}\sqrt{{x}}}}}}\:=\mathrm{1}\: \\ $$
Commented by Mikael_Marshall last updated on 01/May/19
$${thanks}\:{Sir} \\ $$
Commented by maxmathsup by imad last updated on 01/May/19
$${you}\:{are}\:{welcome}. \\ $$