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lim x→0 ( (27 + x)^(1/3) − 3) / ( 9 − (27 + x)^(2/3)) equals -

1. −1/3
2. 1/6
3. −1/6
4. 1/3

Correct answer: −1/6

Solution

The limit evaluates to -1/6 because as x approaches 0, the expression simplifies using L'Hôpital's rule or algebraic manipulation, revealing that the rate of change in the numerator and denominator leads to this specific value.

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