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Question
Evaluate the following limit:
If `lim_(x -> 1)[(x^4 - 1)/(x - 1)]` = `lim_(x -> "a")[(x^3 - "a"^3)/(x - "a")]`, find all possible values of a
Solution
It is given that
`lim_(x -> 1)[(x^4 - 1)/(x - 1)] `= `lim_(x -> "a")[(x^3 - "a"^3)/(x - "a")]`
∴ 4(1)3 = 3.a2 ...`[because lim_(x -> "a") (x^"n" - "a"^"n")/(x - "a") = "na"^("n" - 1)]`
∴ 4 = 3a2
∴ a2 = `4/3`
∴ a = `± 2/sqrt(3)`
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