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Wolfram Alpha evaluates this limit

$\lim_{x\to \infty } \, \frac{x}{\ln (x)-\ln \left(\frac{1}{x}\right)}$

to be infinity.

But I suspect it could be a real number. What is the correct answer?

  • 0
    Why do you suspect it could be a real number?2012-10-27

3 Answers 3

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Wolfram alpha is right because the denominator is $\ln(x)-\ln(\frac1x)=2\ln x$, which grows slower than $x$.