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Rationalization Method to Remove Indeterminate Form

Find the foll...

Question

Find the following limit.
$lim x \to 2 \frac{x^{2} - x - 6}{x^{2} + 7 x - 10} .$

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Solution

Applying L-Hospital Rule,
$lim x \to 2 \frac{x^{2} - x - 6}{x^{2} + x - 10} = lim x \to 2 \frac{\frac{d}{d x} (x^{2} - x - 6)}{\frac{d}{d x} (x^{2} + 7 x - 10)} = lim x \to 2 \frac{2 x - 1}{2 x + 7} = \frac{3}{11}$

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