Limits at Infinity and Horizontal Asymptotes

I. For the rational function $\frac{2*x^2+3}{x^2-1}$, the horizontal asymptote is $y=2$.

II. The limit $\lim_{x\to\infty} \frac{5*x+1}{2*x+7}$ equals $\frac{5}{2}$.

III. For the function $f(x)= \frac{e^{-x}}{x}$, as $x\to\infty$, the limit is $0$.

Which of these statements are true regarding limits involving infinity?