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Step-by-step Solution

Evaluate the limit of $\frac{\sqrt{x+5}-1\cdot \sqrt{5}}{x}$ as $x$ approaches $0$

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Step-by-step explanation

Problem to solve:

$\lim_{x\to0}\left(\frac{\sqrt{x+5}-\sqrt{5}}{x}\right)$

Learn how to solve limits problems step by step online.

$\lim_{x\to0}\left(\frac{\sqrt{x+5}-\sqrt{5}}{x}\frac{\sqrt{x+5}+\sqrt{5}}{\sqrt{x+5}+\sqrt{5}}\right)$

Unlock this full step-by-step solution!

Learn how to solve limits problems step by step online. Evaluate the limit of ((x+5)^0.5-5^0.5)/x as x approaches 0. Applying rationalisation. Multiplying fractions. Solve the product of difference of squares \left(\sqrt{x+5}-\sqrt{5}\right)\left(\sqrt{x+5}+\sqrt{5}\right). Simplifying.

Answer

$\frac{36}{161}$$\,\,\left(\approx 0.22360679774997896\right)$

Problem Analysis

$\lim_{x\to0}\left(\frac{\sqrt{x+5}-\sqrt{5}}{x}\right)$

Main topic:

Limits

Time to solve it:

~ 0.4 seconds