# Thread: Interesting Limits. #1

1. ## Interesting Limits. #1

Without L'Hospital's Rule, evaulate:

$\lim_{x\to\infty} \frac { x \, ln( \, ln(x+1) \, ) } { ln(x) }$.

2. For large x :

$ln( ln(x+1) ) > 1$

so

$x ln( ln(x+1) ) > x$

so

$\frac { x \, ln( \, ln(x+1) \, ) } { ln(x) } > \frac{x}{ln(x)}
$

which clearly goes to infinity as x goes to infinity