Evaluate the following limits in Exercise: _ x 2 3x^2-x-10 x^2-4 - Vidyadip

Question

Evaluate the following limits in Exercise:$$$\lim\limits_{\text{x} \rightarrow2}\frac{3\text{x}^2-\text{x}-10}{\text{x}^2-4}$

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Answer

At x = 2, the value of the given rational function takes the form $\frac{0}{0}$.
$\therefore\lim\limits_{\text{x}\rightarrow2}\frac{3\text{x}^2-\text{x}-10}{\text{x}^2-4}=\lim\limits_{\text{x}\rightarrow2}\frac{(\text{x}-2)(3\text{x}+5)}{(\text{x}-2)(\text{x}+2)}$
$$$=\lim\limits_{\text{x}\rightarrow2}\frac{3\text{x}+5}{\text{x}+2}$
$=\frac{3(2)+5}{2+2}$
$=\frac{11}{4}$

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