** Final Answer

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** Step-by-step Solution **

Problem to solve:

** Specify the solving method

We could not solve this problem by using the method: **Limits by rationalizing**

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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

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Learn how to solve problems step by step online. Find the limit (x)->(10)lim(((x+6)^1/2-4)/(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'H么pital'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. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}.

** Final Answer

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