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Step-by-step Solution

Evaluate the limit of $\frac{\sqrt{n+2}-1\cdot \sqrt{2}}{n}$ as $x$ approaches $0$

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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.

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

Unlock this full step-by-step solution!

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.

Answer

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

Problem Analysis

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

Main topic:

Limits

Related formulas:

1. See formulas

Time to solve it:

~ 0.06 seconds