# Find lim_x to 1 f(x) if lim_x to 1 f(x)-8 x-1 =10.

## Question:

Find {eq}\displaystyle \lim_{x\ \to\ 1} f(x)\ {/eq} if

{eq}\displaystyle \lim_{x\ \to\ 1} \frac{f(x)-8}{x-1}=10. {/eq}

## Limit of the quotient of functions:

When calculating the limit of the quotient of functions, it is important to consider the property: The limit of the quotient is equal to the quotient of the limits under the assumption that the limit of the denominator is different from zero

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Taking into account, the limit: {eq}\mathop {\lim }\limits_{x \to 1} \frac{{f\left( x \right) - 8}}{{x - 1}} {/eq} exist and the limit {eq}\mathop...

How to Determine if a Limit Does Not Exist

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Chapter 4 / Lesson 9
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Learn what the limit of a function is and how to know if a limit does not exist. Review different types of limits and how to find limits algebraically.