Limits & Continuity · Special Limits
Limit of (cos x - 1)/x
A special limit related to the derivative of cosine at x = 0.
- 0 variables
- 2 worked examples
- 18 in Limits & Continuity
Worked examples
Find lim(x→0) (cos x - 1)/x².
- Use the identity cos x - 1 = -2 sin²(x/2)
- -2 sin²(x/2)/x² = -2 · [sin(x/2)]²/x² = -(1/2) · [sin(x/2)/(x/2)]²
- As x→0, sin(x/2)/(x/2) → 1
Answer: -1/2
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Find lim(x→0) (1 - cos x)/(x sin x).
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Practice
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