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This question already has an answer here:

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

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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

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