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lim-x-x-x-x-x-




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

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