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Rationalization Method to Remove Indeterminate Form

Evaluate lim...

Question

Evaluate
$lim x \to 1 \frac{x^{2} - 3 x + 2}{x - 1}$

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Solution

${lim}_{x \to 1} \frac{x^{2} - 3 x + 2}{x - 1}$ on using L Hospital rule
${lim}_{x \to 1} \frac{\frac{d}{d x} (x^{2} - 3 x + 2)}{\frac{d}{d x} (x - 1)} = {lim}_{x \to 1} \frac{2 x - 3}{1} = 2 \times 1 - 3 = - 1$

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