What is ?
Answer and explanation
Correct answer: D.
- Step 1: Direct substitution yields the indeterminate form . Apply L'Hôpital's rule by differentiating numerator and denominator: .
- Step 2: Evaluating at again gives . Apply L'Hôpital's rule a second time: .
- Step 3: Evaluate the limit: .
Answer
.
Why not the others: Other values apply L'Hopital's rule only once while the limit remains indeterminate, or drop powers of 3 from the exponential chain rule.
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