allerylim_(x→0) (1 - cos x)/x² =
A1/2
B2
C1
D0
Answer & Solution
Correct answer: A. 1/2
Use 1 - cos x = 2 sin²(x/2).
Then (1 - cos x)/x² = 2 × (sin(x/2)/x)² × 1 = (1/2) × (sin(x/2)/(x/2))².
As x → 0, sin(x/2)/(x/2) → 1, so limit = 1/2.
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