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Question
\[\lim_{x \to 1} \frac{x^{15} - 1}{x^{10} - 1}\]
Solution
\[\lim_{x \to 1} \left[ \frac{x^{15} - 1}{x^{10} - 1} \right]\]
\[ = \lim_{x \to 1} \left[ \frac{x^{15} - \left( 1 \right)^{15}}{x - 1} \times \frac{x - 1}{x^{10} - \left( 1 \right)^{10}} \right]\]
\[ = \frac{15 \left( 1 \right)^{15 - 1}}{10 \left( 1 \right)^{10 - 1}}\]
\[ = \frac{3}{2}\]
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