Project ForgeEngineering Mathematics
Calculus
GATE 2014
Medium
Lt(x→0) (x − sin x)/(1 − cos x) is
- 0
- B1
- C3
- Dnot defined
Explanation
Using small-angle Taylor expansions: x − sin x ≈ x³/6 and 1 − cos x ≈ x²/2. The ratio ≈ (x³/6)/(x²/2) = x/3, which → 0 as x→0.
Source: GATE ME 2014 (Session 1 / Set-1) (2014)
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