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Algebra of Limits

Solve limx ...

Question

Solve $lim x \to 3 \frac{x^{2} - 9}{x^{3} - 6 x^{2} + 9 x + 1}$

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Solution

$lim x \to 3 \frac{x^{2} - 9}{x^{3} - 6 x^{2} + 9 x + 1}$

$= \frac{3^{2} - 9}{3^{3} - 6 {(3)}^{2} + 9 (3) + 1}$

$= 0$

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