# Solve: {eq}lim \ x \rightarrow 1 ( \frac {3 \sqrt {(x)} -1)}{(\sqrt {(x)} -1)}) {/eq}

## Question:

Solve: {eq}lim \ x \rightarrow 1 ( \frac {3 \sqrt {(x)} -1)}{(\sqrt {(x)} -1)}) {/eq}

## Limit:

Suppose that {eq}u(x) {/eq} is the function which is define in a interval which contain {eq}x=t {/eq}

then limit is define as;

{eq}\mathop {\lim }\limits_{x \to t} u(x) = P {/eq}

here there exist very small number k ssuch that{eq}k>0 {/eq} so that {eq}n>0 {/eq} which states that

{eq}|u(x) - P| < k {/eq}

Whenever {eq}0 < |x - t| < n {/eq}

if {eq}\mathop {\lim }\limits_{x \to {t^ + }} u(x) = {P_1} {/eq} and {eq}\mathop {\lim }\limits_{x \to {t^ - }} u(x) = {P_2} {/eq} and {eq}{P_1} \ne {P_2} {/eq} then

Limit does not exist.

## Answer and Explanation: 1

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Given that: {eq}\displaystyle \mathop {\lim }\limits_{x \to 1} \left( {\frac{{(3\sqrt {(x)} - 1)}}{{(\sqrt {(x)} - 1)}}} \right) {/eq}

{eq}\dis...

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#### Learn more about this topic:

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.