# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve limits problems step by step online.

$\frac{0}{0}$

Learn how to solve limits problems step by step online. Evaluate the limit of ((5+x)^0.5-5^0.5)/x as x approaches 0. If we directly evaluate the limit \lim_{x\to 0}\left(\frac{\sqrt{5+x}-\frac{5}{\sqrt{5}}}{x}\right) as x tends to 0, we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately. After deriving both the numerator and denominator, the limit results in. Any expression divided by one (1) is equal to that same expression.

$\frac{1}{2\sqrt{5}}$$\,\,\left(\approx 0.22360679774997896\right)$
$\lim_{x\to0}\left(\frac{\sqrt{5+x}-\sqrt{5}}{x}\right)$