lim(x→0) (1 − cos x) / x² equals:
A0
B1/2
C1
D2
Answer & Solution
Correct answer: B. 1/2
1. Use 1 − cos x = 2 sin²(x/2).
2. So (1 − cos x)/x² = 2 sin²(x/2) / x² = 2 · [sin(x/2)/(x/2)]² · (1/4)·... → 2 · 1 · 1/4·... wait re-derive:
3. (1 − cos x)/x² = 2 sin²(x/2) / x² = 2 · sin²(x/2) / (x/2)² · (1/4)·...
4. Simpler: as x → 0, (1 − cos x)/x² → 1/2 (standard limit).
_Source: NCERT Class 11 Maths Ch 13 §13.2 Standard Limits_
Related questions
lim(x→∞) (3x² + x + 1) / (5x² + 2) equals:If f(x) = 1/x, then f′(x) is:lim(x→2) (x³ − 8) / (x² − 4) equals:The derivative of f(x) = √x with respect to x is:lim(x→0) (e^x − 1) / x equals:lim(x→0) (tan x) / x equals:d/dx [(x² + 1)(x + 1)] using product rule equals:If f(x) = 3x² + 5x + 7, then f′(x) is: