Evaluate _ x 3 x^4 - 81 2 x^2 - 5x - 3 - Vidyadip

Question

Evaluate $\mathop {\lim }\limits_{x \to 3} \frac{{{x^4} - 81}}{{2{x^2} - 5x - 3}}$

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Answer

Here $\mathop {\lim }\limits_{x \to 3} \frac{{{x^4} - 81}}{{2{x^2} - 5x - 3}}\left[ {\frac{0}{0}{\text{from}}} \right]$
$= \mathop {\lim }\limits_{x \to 3} \frac{{({x^2} + 9)(x + 3)(x - 3)}}{{(x - 3)(2x + 1)}}$
$= \mathop {\lim }\limits_{x \to 3} \frac{{({x^2} + 9)(x + 3)}}{{(2x + 1)}} = \frac{{({3^2} + 9)(3 + 3)}}{{(2 \times 3 + 1)}} = \frac{{108}}{7}$

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