Jan 30, 2013 Thread starter #1 Y Yankel Active member Jan 27, 2012 398 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 ! [tex]\lim_{x\to 0^{+}}x^{3}\cdot (ln(x))^{2}[/tex]

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 ! [tex]\lim_{x\to 0^{+}}x^{3}\cdot (ln(x))^{2}[/tex]

Jan 30, 2013 Admin #2 M MarkFL Administrator Staff member Feb 24, 2012 13,775 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?

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?