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Question
if `lim_(x -> 2) (x^"n"- 2^"n")/(x - 2)` = 80 then find the value of n.
Solution
`lim_(x -> 2) (x^"n"- 2^"n")/(x - 2)` = 80
∴ n(2)n–1 = 80 ...`[lim_(x -> "a") (x^"n" - "a"^"n")/(x - "a") = "na"^("n" - 1)]`
∴ n(2)n–1 = 5 x 16
= 5 x (2)4
∴ n(2)n –1 = 5 x (2)5–1
∴ n = 5
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