How can I accurately compute $\sqrt{x + 2} −\sqrt{x}$ when $x$ is large? How can the values of the function $f(x) = \sqrt{x + 2} −\sqrt{x}$ be computed accurately when $x$ is large?
I have tried using Matllab. I am not able to understand when $x$ will be large.

Recall that when $t$ is small, $\sqrt{1+t}\approx 1 + t/2$. It follows that, for $x$ large and positive,
$$
f(x)= \sqrt{x}(\sqrt{1+2/x}-1)\approx 1/\sqrt{x},
$$
in the sense that $f(x)\sqrt{x}\rightarrow 1$ as $x\rightarrow \infty$.
