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

Question:

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