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# Evaluate the following limits  $\lim\limits_{x \to 2} \large\frac{3x^2-x-10}{x^2-4}$

$\begin{array}{1 1} \large\frac{11}{4} \\ \frac{11}{2} \\ 0 \\ \infty \end{array}$

When $x = 2 \rightarrow$ the rational function takes the value $\large\frac{0}{0}.$
$\Rightarrow \lim\limits_{x \to 2} \large\frac{3x^2-x-10}{x^2-4}$ $= \lim\limits_{x \to 2} \large\frac{(x-2)(3x+5)}{(x-2)(x+2)}$
$= \lim\limits_{x \to 2} \large\frac{3x+5}{x+2}$
$= \large\frac{3(2)+5}{2+2}$
$= \large\frac{11}{4}$
edited May 16, 2014