# Thread: Limit problems with e and ln

1. ## Limit problems with e and ln

$\lim_{x \to +\infty} \frac {x^4}{e^x}$

$\lim_{x \to +\infty} \frac {\ln x}{x}$

Can anyone show me how these limit reaches to 0?

2. Originally Posted by chengbin
$\lim_{x \to +\infty} \frac {x^4}{e^x}$

$\lim_{x \to +\infty} \frac {\ln x}{x}$

Can anyone show me how these limit reaches to 0?
Use l'Hospital's rule 4 times for the first limit and once for the second.

3. Originally Posted by chengbin
$\lim_{x \to +\infty} \frac {x^4}{e^x}$

$\lim_{x \to +\infty} \frac {\ln x}{x}$

Can anyone show me how these limit reaches to 0?
$\lim_{x \to +\infty} \frac {x^4}{e^x} = 0 = \lim_{x \to +\infty} \frac {\ln x}{x}$, because you know that

$x^4 < e^x \ \& \ ln x < x$ for big x

Proof by using L'Hospital