Question

Cat este limita din ln x/1-x ? (x tinde la infinit )

Answer 1

$\lim_{x \to \infty}\limits{\dfrac{\text{ln}x}{1-x}} \overset{\boxed{\dfrac{\infty}{-\infty}}\Big{(L'h\Big)}}{=} \\ \\ = \lim_{x \to \infty}\limits{\dfrac{(\text{ln}x)'}{(1-x)'}} = \\ \\= \lim_{x \to \infty}\limits{\dfrac{\dfrac{1}{x}}{-1}} = \\ \\= \lim_{x \to \infty}\limits{-\dfrac{1}{x}} = \\ \\ =0$