Finding asymptotes of exponential function and one-sided limit Find the asymptotes of
$$
\lim_{x \to \infty}x\cdot\exp\left(\dfrac{2}{x}\right)+1.
$$
How is it done?

$$\lim_{x \to \infty}\frac d{dx}\left( x\cdot\exp\left(\dfrac{2}{x}\right)+1\right)=\lim_{x \to \infty}\exp\left(\frac2x\right)-\frac{2\exp\left(\frac2x\right)}{x}=1$$
therefore your function rises like $x$ asymptotically.
