# Limit problem: $\sqrt{x+1} - \sqrt{x}$ as $x$ approaches infinity [duplicate]

I know it is extremely basic but I am stuck on this limit:

$$\lim_{x \to \infty} \sqrt{x+1} - \sqrt{x}$$

I have no idea how to proceed. Hints or full solutions are welcome.

## marked as duplicate by Servaes, drhab, Tom-Tom, user91500, jameselmoreSep 23 '15 at 12:19

Hint: Multiply by $$\frac{\sqrt{x+1}+\sqrt{x}}{\sqrt{x+1}+\sqrt{x}}$$