i want to find the horizontal asymptotes of f(x)=x-2ln x for x>0
but how can i do that?
Horizontal asymptotes occur at $\displaystyle \displaystyle y = \lim_{x \to \pm \infty} f(x)$. In this case, $\displaystyle x > 0$, so horizontal asymptotes occur at only $\displaystyle \displaystyle y = \lim_{x \to + \infty} f(x)$.