Would anyone please give me a epsilon-delta proof: when $x$ approaches to infinity, $$x\sqrt{x+2}-\sqrt x=\infty\;.$$
What I did was:
$$\left(x\sqrt{x+2}-\sqrt x\right)\cdot\frac{\sqrt{x+2}+\sqrt x}{\sqrt{x+2}+\sqrt x} =\frac{2x}{\sqrt{x+2}+\sqrt x}$$
Then, what is the next step?