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The expression \(\lim_{x\to 0} \frac{x^\alpha - 1}{\alpha}\) is equal to

1. log x
2. 0
3. x log x
4. ∞

Correct answer: log x

Solution

The expression as written has a mismatch: the limit is taken with respect to \(x\), but \(\alpha\) appears in the denominator. The standard intended limit is \(\lim_{\alpha\to 0} \frac{x^\alpha-1}{\alpha}=\ln x\), which matches the option 'log x'.

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