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Question
If \[\lim_{x \to a} \frac{x^5 - a^5}{x - a} = 405,\]find all possible values of a.
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Solution
\[\lim_{x \to a} \left[ \frac{x^5 - a^5}{x - a} \right] = 405\]
\[ \Rightarrow 5 a^4 = 405\]
\[ \Rightarrow a^4 = 81\]
\[ \Rightarrow a^2 = 9\]
\[ \Rightarrow a = \pm 3\]
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