What is the limit of (1 - cos x) / x^2 as x approaches 0?
Answer and explanation
Correct answer: D. 1/2
- Step 1: Applying L'Hopital's rule: derivative of numerator is sin x, denominator is 2x. Lim (sin x) / (2x). Step 2. Second L'Hopital step: (cos x) / 2 as x -> 0 gives cos(0)/2 = 1/2. Answer: 1/2. Why not the others: 1 forgets factor 2 in denominator; 0 assumes numerator evaluates to 0; 2 inverts the fraction.
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