Evaluate using L'Hopital's Rule.
Answer and explanation
Correct answer: B.
Numerator derivative: .
Denominator derivative: .
Numerator derivative: .
Denominator derivative: .
Denominator derivative: .
Numerator derivative: .
Denominator derivative: .
- Step 1: Direct substitution gives . Apply L'Hopital's Rule once: differentiate numerator and denominator.
- Step 2: Direct substitution into still gives . Apply L'Hopital's Rule a second time:
- Step 3: Evaluate the limit: .
Answer
.
Why not the others: '0' halts after the first differentiation at ; '1' omits the chain rule factors of 2 from the exponent ; '' assumes higher order terms in the denominator cause divergence.
Practise more Differentiation.
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