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Factorization Method Form to Remove Indeterminate Form

lim x → 02 x2...

Question

${lim}_{x \to 0} \frac{2 x^{2} + 3 x + 4}{x^{2} + 3 x + 2}$

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Solution

${lim}_{x \to 0} \frac{2 x^{2} + 3 x + 4}{x^{2} + 3 x + 2}$

$= {lim}_{x \to 0} \frac{2 x^{2} + 3 x + 4}{(x + 2) (x + 1)} = \frac{2 (0) + 3 (0) + 4}{(0 + 2) (0 + 1)}$

$= \frac{4}{4} = 2.$

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