Step-by-step Solution

Find the limit $\lim_{x\to10}\left(\frac{\sqrt{x+6}-4}{x-10}\right)$

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Step-by-step solution

Problem to solve:

$\lim_{x\to\:10}\left(\frac{\sqrt{x+6}-4}{x-10}\right)$

Solving method

Learn how to solve limits problems step by step online.

$\frac{0}{0}$

Unlock this full step-by-step solution!

Learn how to solve limits problems step by step online. Find the limit (x)->(10)lim(((x+6)^0.5-4)/(x-10)). If we directly evaluate the limit \lim_{x\to 10}\left(\frac{\sqrt{x+6}-4}{x-10}\right) as x tends to 10, 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.

Final Answer

$\frac{1}{8}$$\,\,\left(\approx 0.125\right)$
$\lim_{x\to\:10}\left(\frac{\sqrt{x+6}-4}{x-10}\right)$

Main topic:

Limits

Related Formulas:

4. See formulas

Time to solve it:

~ 0.05 s