Find the limit of LIM (x → 1) [(^ 3 √ x-1) / (x-1)]

Method 1: LIM (x → 1) [x ^ (1 / 3) - 1] / (x-1) is exactly the derivative function of F (x) = x ^ (1 / 3) at x = 1, f '(x) = 1 / [3x ^ (2 / 3)], so LIM (x → 1) [x ^ (1 / 3) - 1] / (x-1) = f' (1) = 1 / 3. Method 2: because it is in the form of 0 / 0, using the law of Robita, LIM (x → 1) [x ^ (1 / 3) - 1] / (x-1) = LIM (x → 1)

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