Maharashtra State BoardHSC Arts 11th
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Evaluate the following limit: If limx→1[x4-1x-1] = limx→a[x3-a3x-a], find all possible values of a - Mathematics and Statistics

Sum

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

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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)`

  Is there an error in this question or solution?
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