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Question
\[\lim_{x \to 4} \frac{x^3 - 64}{x^2 - 16}\]
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Solution
\[\lim_{x \to 4} \left[ \frac{x^3 - 64}{x^2 - 16} \right]\]
\[ = \lim_{x \to 4} \left[ \frac{x^3 - 64}{x - 4} \times \frac{x - 4}{x^2 - 16} \right]\]
\[ = \lim_{x \to 4} \left[ \frac{x^3 - 4^3}{x - 4} \times \frac{x - 4}{x^2 - 4^2} \right]\]
\[ = 3 \left( 4 \right)^{3 - 1} \times \frac{1}{2 \left( 4 \right)^{2 - 1}}\]
\[ = \frac{3 \times 16}{2 \times 4}\]
\[ = 6\]
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