下列计算极限的过程正确的是
A. $\lim _{x \rightarrow+\infty}\left(\sqrt{x^2+1}-x\right)=\lim _{x \rightarrow+\infty} \sqrt{x^2+1}-\lim _{x \rightarrow+\infty} x=\infty-\infty=0$.
B. $\lim _{x \rightarrow 0} x \sin \frac{1}{x}=\lim _{x \rightarrow 0} x \cdot \lim _{x \rightarrow 0} \sin \frac{1}{x}=0$.
C. $\lim _{x \rightarrow+\infty} \frac{\sqrt{x}}{x}=\frac{\lim _{x \rightarrow+\infty} \sqrt{x}}{\lim _{x \rightarrow+\infty} x}=\frac{\infty}{\infty}=1$.
D. $\lim _{x \rightarrow 0} \frac{x^2-x}{x^2+x}=\lim _{x \rightarrow 0} \frac{x(x-1)}{x(x+1)}=\lim _{x \rightarrow 0} \frac{x-1}{x+1}=\frac{\lim _{x \rightarrow 0}(x-1)}{\lim _{x \rightarrow 0}(x+1)}=\frac{-1}{1}=-1$.