D

- Hướng dẫn giải

Chọn D

$\underset{x\to +\infty }{\lim }x\left(\sqrt{x^2+1}-x\right)=\underset{x\to +\infty }{\lim }x\frac{x^2+1-x^2}{\sqrt{x^2+1}+x}=\underset{x\to +\infty }{\lim }\frac{x}{x\sqrt{1+\frac{1}{x^2}}+x.1}=\frac{1}{1+1}=\frac{1}{2}$