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Question
\[\lim_{x \to 3} \frac{x^4 - 81}{x^2 - 9}\]
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Solution
\[\lim_{x \to 3} \left[ \frac{x^4 - 81}{x^2 - 9} \right]\]
\[\text{ It is of the form } \frac{0}{0} . \]
\[ \lim_{x \to 3} \left[ \frac{\left( x^2 \right)^2 - 9^2}{x^2 - 9} \right]\]
\[ = \lim_{x \to 3} \left[ \frac{\left( x^2 - 9 \right)\left( x^2 + 9 \right)}{x^2 - 9} \right]\]
\[ = \lim_{x \to 3} \left( x^2 + 9 \right)\]
\[ = 3^2 + 9\]
\[ = 18\]
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