Project ForgeEngineering Mathematics
Calculus
GATE 2012
Easy
lim(x→0) [(1−cos x)/x²] is
- A1/4
- 1/2
- C1
- D2
Explanation
Using the small-angle series cos x ≈ 1−x²/2+x⁴/24−..., 1−cos x ≈ x²/2, so (1−cos x)/x² → 1/2 as x→0. (Equivalently, apply L'Hôpital's rule twice: sin x/(2x) → cos x/2 → 1/2.)
Source: GATE ME 2012 (Booklet Code A) (2012)
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