Question Number 195697 by sonukgindia last updated on 08/Aug/23
Answered by MM42 last updated on 08/Aug/23
$${if}\:\:{mean}\:\:\:{lim}_{{x}\rightarrow\infty} \:\sqrt[{{x}}]{{x}\:}\:\:{then} \\ $$$${A}={lim}_{{x}\rightarrow\infty} \:\sqrt[{{x}}]{{x}} \\ $$$$\Rightarrow{lnA}={lim}_{{x}\rightarrow\infty} \:\frac{{lnx}}{{x}}\:=\mathrm{0}\Rightarrow{A}=\mathrm{1} \\ $$
Commented by Frix last updated on 08/Aug/23
$$\mathrm{But}\:\sqrt[{\infty}]{\infty}\:``=''\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{{n}}]{{n}!}\:=\infty \\ $$