so i have this problem and i know that it converges to 0 but i dont know why
can someone help me
lim x->(infinity) (lnx)^3/x^2
Hi Lone21,
Since the numerator and the denominator both go to inf. as x goes to inf.
We can apply L'Hospital's Rule:
As $\displaystyle {x\rightarrow infinity}$, $\displaystyle \lim \frac{(\ln x)^3}{x^2}=\lim \frac{3(ln x)^2 * \frac{1}{x}}{2x}= \lim \frac{3(ln x)^2 }{2x^2} =... $
Just keep applying L'Hospital's Rule and simplify your answer in each step.