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Dangerous Limit

Calculus Level 3

\[ \Large \displaystyle \xi(k) = \lim_{x\rightarrow \infty} \left( \dfrac{ (k x)!}{x^{kx}} \right)^{1/x} , \quad k \in \mathbb N\]

Choose the correct option.

\[\xi(2) = \dfrac{4}{e}\] None of these \[\xi(2) =\dfrac{1}{e}\] \[\\xi(1) = \dfrac{2}{e}\] \[\xi(1) = \dfrac{1}{e}\]

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Excel in math and science

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by Akhil Bansal

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