Question:
Evaluate the Given limit: $\lim _{x \rightarrow 2} \frac{3 x^{2}-x-10}{x^{2}-4}$
Solution:
At $x=2$, the value of the given rational function takes the form $\frac{0}{0}$.
$\therefore \lim _{x \rightarrow 2} \frac{3 x^{2}-x-10}{x^{2}-4}=\lim _{x \rightarrow 2} \frac{(x-2)(3 x+5)}{(x-2)(x+2)}$
$=\lim _{x \rightarrow 2} \frac{3 x+5}{x+2}$
$=\frac{3(2)+5}{2+2}$
$=\frac{11}{4}$
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