lim as x goes to 0 from the positive direction of sqrt(x)log(x)

correct me if I'm wrong but the actual limit at x=o does not exist yes?

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- Apr 18th 2010, 01:04 AMNicholasLimit question (please help)
lim as x goes to 0 from the positive direction of sqrt(x)log(x)

correct me if I'm wrong but the actual limit at x=o does not exist yes? - Apr 18th 2010, 02:29 AMRandom Variable
$\displaystyle \lim_{x \to 0^{+}} \sqrt{x} \ln x = \lim_{x \to 0+} \frac{\ln x}{\frac{1}{\sqrt{x}}} = \lim_{x \to 0^{+}} \frac{\frac{1}{x}}{\frac{-1}{2x^{\frac{3}{2}}}} = \lim_{x \to 0^{+}} -2 \sqrt{x} = 0$

- Apr 19th 2010, 02:03 AMNicholas
Thanks a heap, but does the limit at x=0 exist?

- Apr 19th 2010, 02:53 AMHallsofIvy
Does 0 exist?