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Question

Evaluate the Given limit: $lim x \to 3 \frac{x^{4} - 81}{2 x^{2} - 5 x - 3}$

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Solution

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$lim x \to 3 \frac{x^{4} - 81}{2 x^{2} - 5 x - 3} = lim x \to 3 \frac{(x - 3) (x + 3) (x^{2} + 9)}{(x - 3) (2 x + 1)}$
$= lim x \to 3 \frac{(x + 3) (x^{2} + 9)}{2 x + 1} = \frac{(3 + 3) (3^{2} + 9)}{2 (3) + 1} = \frac{6 \times 18}{7} = \frac{108}{7}$

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