** Final Answer

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** Step-by-step Solution **

Problem to solve:

** Specify the solving method

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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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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

Learn how to solve limits by direct substitution problems step by step online.

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Learn how to solve limits by direct substitution 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'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. 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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