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If 0ltlog(e)xltsqrt(x) for all xlt1, the...

If `0ltlog_(e)xltsqrt(x)` for all `xlt1,` then find the value of `lim_(xtooo) (log_(e)x)/(x).`

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To solve the problem, we need to find the limit: \[ \lim_{x \to \infty} \frac{\log_e x}{x} \] Given that \(0 < \log_e x < \sqrt{x}\) for all \(x < 1\), we can analyze the limit step by step. ...
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