Evaluate _ x 2 3 x^2 - x - 10 x^2 - 4 - Vidyadip

Question

Evaluate $\mathop {\lim }\limits_{x \to 2} \frac{{3{x^2} - x - 10}}{{{x^2} - 4}}$

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Answer

Here $\mathop {\lim }\limits_{x \to 2} \frac{{3{x^2} - x - 10}}{{{x^2} - 4}}\left[ {\frac{0}{0}{\text{from}}} \right]$
$= \mathop {\lim }\limits_{x \to 2} \frac{{(x - 2)(3x + 5)}}{{(x + 2)(x - 2)}}$
$= \mathop {\lim }\limits_{x \to 2} \frac{{3x - 5}}{{x + 2}} = \frac{{6 + 5}}{{2 + 2}} = \frac{{11}}{4}$

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