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Question
Find the positive integer n so that `lim_(x -> 3) (x^n - 3^n)/(x - 3)` = 108.
Solution
We have `lim_(x -> 3) (x^n - 3^n)/(x - 3) = n(3)^(n - 1)`
Therefore, `n(3)^(n - 1)` = 108
= 4(27)
= `4(3)^(4 - 1)`
Comparing, we get
n = 4
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