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Home  >>  CBSE XI  >>  Math  >>  Limits and Derivatives
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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} $

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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}$
answered Apr 3, 2014 by thanvigandhi_1
edited May 16, 2014 by balaji.thirumalai
 

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