Hi, I'm having trouble starting this problem. Someone suggested using L'Hospital's rule but I can't figure out how to apply that here. Anyway, here's the problem, any help would be appreciated. Thanks in advance.
Lim x-->0+
X ^ ( -1 / ln(x) )
Hi, I'm having trouble starting this problem. Someone suggested using L'Hospital's rule but I can't figure out how to apply that here. Anyway, here's the problem, any help would be appreciated. Thanks in advance.
Lim x-->0+
X ^ ( -1 / ln(x) )
take the natural log
$\displaystyle \lim_{x \to 0^{+}} \ln \Big(x^{\frac {\text{-}1}{ln(x)}}\Big) = \lim_{x \to 0^{+}} \frac {\text{-}1}{\ln(x)} \ln(x)$ $\displaystyle = \text{-}1 $
therefore, $\displaystyle \lim_{x \to 0^{+}} x^{\frac {\text{-}1}{ln(x)}} = e^{-1} = \frac {1}{e} $