How do you find the Limit of (lnx)^3/x^2 as x approaches infinity?

Jun 3, 2018

${\lim}_{x \to + \infty} {\left(\ln x\right)}^{3} / {x}^{2} = 0$

Explanation:

${\lim}_{x \to + \infty} {\left(\ln x\right)}^{3} / {x}^{2} {=}_{D L H}^{\left(\frac{+ \infty}{+ \infty}\right)}$

${\lim}_{x \to + \infty} \frac{\frac{3 {\left(\ln x\right)}^{2}}{x}}{2 x} =$

${\lim}_{x \to + \infty} \frac{3 {\left(\ln x\right)}^{2}}{2 {x}^{2}} =$

$\frac{3}{2} {\lim}_{x \to + \infty} {\left(\ln \frac{x}{x}\right)}^{2} = 0$

because

• ${\lim}_{x \to + \infty} \ln \frac{x}{x} {=}_{D L H}^{\left(\frac{+ \infty}{+ \infty}\right)}$

${\lim}_{x \to + \infty} \frac{1}{x} {=}^{\left(\frac{1}{+ \infty}\right)} = 0$