# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\lim_{x\to0}\left(\frac{\sqrt{n+2}-\sqrt{2}}{n}\right)$

Learn how to solve limits problems step by step online.

$\lim_{x\to0}\left(\frac{\sqrt{n+2}-\sqrt{2}}{n}\frac{\sqrt{n+2}+\sqrt{2}}{\sqrt{n+2}+\sqrt{2}}\right)$

Learn how to solve limits problems step by step online. Evaluate the limit of ((n+2)^0.5-2^0.5)/n as x approaches 0. Applying rationalisation. Multiplying fractions. Solve the product of difference of squares \left(\sqrt{n+2}-\sqrt{2}\right)\left(\sqrt{n+2}+\sqrt{2}\right). Simplifying.

$\frac{1}{\sqrt{n+2}+\sqrt{2}}$

### Problem Analysis

$\lim_{x\to0}\left(\frac{\sqrt{n+2}-\sqrt{2}}{n}\right)$

Limits

~ 0.06 seconds