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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.

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

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