Evaluate limx→∞x!xx\lim_{x \to \infty} \frac{x!}{x^x}limx→∞xxx! (informally, using Stirling's approximation x!≈2πx(x/e)xx! \approx \sqrt{2\pi x}(x/e)^xx!≈2πx(x/e)x).
111
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∞\infty∞