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If lim x→1 (x⁴ − 1)/(x − 1) = lim x→k (x³ − k³)/(x² − k²), then k is:

1. 3/2
2. 8/3
3. 4/3
4. 3/8

Correct answer: 8/3

Solution

The limit on the left can be simplified using L'Hôpital's rule or by factoring, resulting in 4. The limit on the right can also be simplified, and setting it equal to 4 allows us to solve for k, leading to the conclusion that k must be 8/3.

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