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Factorization Method Form to Remove Indeterminate Form

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Question

Evaluate : ${lim}_{x \to 2} \frac{3 x^{2} - x - 10}{x^{2} - 4}$

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Solution

${lim}_{x \to 2} \frac{3 x^{2} - x - 10}{x^{2} - 4}$

$= {lim}_{x \to 2} \frac{3 x^{2} - 6 x + 5 x - 10}{(x - 2) (x + 2)}$

$= {lim}_{x \to 2} \frac{3 x (x - 2) + 5 (x - 2)}{(x - 2) (x + 2)}$

$= {lim}_{x \to 2} \frac{(x - 2) (3 x + 5)}{(x - 2) (x + 2)}$

$= {lim}_{x \to 2} \frac{(3 x + 5)}{(x + 2)}$

$= \frac{3 \times 2 + 5}{2 + 2} = \frac{6 + 5}{4} = \frac{11}{4}$

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Q. Evaluate the Given limit:

lim x \to 2 \frac{3 x^{2} - x - 10}{x^{2} - 4}

lim x \to 2 \frac{3 x^{2} - x - 10}{x^{2} - 4}

∴ {lim}_{x \to 2} \frac{3 x^{2} - x - 10}{x^{2} - 4}

lim x \to 2 \frac{x^{2} - 4}{x - 2}

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