Answer
$\infty$
Work Step by Step
We evaluate the limit
\begin{aligned}
\lim_{x\to\infty}(2 \sqrt{x}-\sqrt{x+2} )&=\lim_{x\to\infty}(2 \sqrt{x}-\sqrt{x+2}) \frac{2 \sqrt{x}+\sqrt{x+2}}{2 \sqrt{x}+\sqrt{x+2}} \\
&=\lim_{x\to\infty}\frac{4 x-(x+2)}{2 \sqrt{x}+\sqrt{x+2}}\\
&=\lim_{x\to\infty}\frac{3 x-2}{2 \sqrt{x}+\sqrt{x+2}}\\
&=\infty
\end{aligned}
