Question

De ce $\lim_{x \to \infty} \frac{x}{ e^{x}+1 }$=0?

Answer 1

Este nedeterminare de forma infinit /infinit, aplicam regula lui L'Hospital :
$\lim_{x \to \infty} \frac{x}{e^x+1}= \lim_{x \to \infty} \frac{1}{e^x}= \frac{1}{\infty}=0$

Answer 2

$\lim_{x \to \infty} \frac{x}{e^x+1}= \frac{infinit}{infinit}= \lim_{x \to \infty} \frac{x'}{(e^x+1)'} = \lim_{x \to \infty} \frac{1}{e^x} = \frac{1}{infinit}=0$