MHB Limit Calculation Help: x^3(ln(x))^2

[Yankel]

Hello

I need some help with this limit. I know I should use the L'hopital rule, but not sure how to do it...any help will be appreciated !

\lim_{x\to 0^{+}}x^{3}\cdot (ln(x))^{2}

 

[MarkFL]

I notice this is the indeterminate form $0\cdot\infty$, so I would recommend writing it as:

$\displaystyle \lim_{x\to0^{+}}\frac{\ln^2(x)}{x^{-3}}$

Now we have the indeterminate form $\dfrac{\infty}{\infty}$ and we may apply L'Hôpital's rule.

Can you proceed?