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Question
If \[\lim_{x \to a} \frac{x^9 - a^9}{x - a} = \lim_{x \to 5} \left( 4 + x \right),\] find all possible values of a.
Solution
\[\lim_{x \to a} \left[ \frac{x^9 - a^9}{x - a} \right] = \lim_{x \to 5} \left( 4 + x \right)\]
\[ \Rightarrow 9 a^{9 + 1} = 9\]
\[ \Rightarrow a^8 = 1\]
\[ \Rightarrow a = \pm 1\]
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