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3 problems match “Stirling's approximation”. Clear

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1. Limit of xth root of factorial over x ●●●○○ 50 ptsFind the value of $\lim_{n\to\infty} \frac{\sqrt[n]{n!}}{n}$, where $n$ is a positive integer. Round to two decimal places.
2. Limit of nth root of factorial over n ●●●○○ 50 ptsFind $\lim_{n\to\infty} \frac{(n!)^{1/n}}{n}$. Round to three decimal places.
3. Limit of a central binomial ratio ●●●○○ 50 ptsFind $\lim_{n \to \infty} \frac{(2n)!\,\sqrt{n}}{(n!)^2\,4^n}$. Round to two decimal places.