Question

Compute the Limit
`\lim_(x \to \infty) ((log(x))^(2) )/(x)`

Answer 1

By applying L'Hopital's rule twice,

`\displaystyle \lim_(x\to\infty) (\log^2(x))/(x) = \lim_(x\to\infty) \frac{\frac{2\log(x)}x}1 \\\\ = \lim_(x\to\infty) \frac{2\log(x)}x \\\\ = \lim_(x\to\infty) \frac{\frac2x}1 \\\\ = \lim_(x\to\infty)\frac2x = \boxed{0}`