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Question
If `lim_(x->2) (x^n - 2^n)/(x-2) = 448`, then find the least positive integer n.
Solution
`lim_(x->2) (x^n - 2^n)/(x-2) = 448`
i.e., n 2n-1 = 7 × 26
n × 2n-1 = 7 × 27-1
∴ n = 7
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