How to compute $\lim_{x \to \infty} \sqrt{x}(e^{-1/x}-1)$? I need to compute $$\lim_{x \to \infty} \sqrt{x}(e^{-1/x}-1)$$ using L'Hôpital's rule. Please hint me how to do it.
Thanks!

$$\lim_{x \to \infty} \sqrt{x}(e^{-\dfrac{1}{x}}-1)=\lim_{x \to \infty}\frac{(e^{-\dfrac{1}{x}}-1)}{\frac1{\sqrt{x}}}$$
