Answer
$2$
Work Step by Step
Factor each polynomial:
$$\lim_{x\to 1^-}\frac{x^3-1}{x-1}\\=\lim_{x\to 1^-}\frac{x(x-1)(x+1)}{x-1}.$$
Cancel the common factors: $$\lim_{x\to 1^-}x(x+1)\\=1(1+1)=2$$
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