2022 Medium
Single Choice
Marks: 4.00 / −2.00
Evaluate: \[ \lim_{x \to 0} \frac{1 - \cos x}{x^2} \]
- A. \( \dfrac{1}{2} \)
- B. 0
- C. 1
- D. \( \infty \)
Correct Option:
- A. \( \dfrac{1}{2} \) ✓ Correct
- B. 0
- C. 1
- D. \( \infty \)
Hint: Use the identity \( 1 - \cos x = 2\sin^2(x/2) \).
Solution:
\( \frac{1-\cos x}{x^2} = \frac{2\sin^2(x/2)}{x^2} \to \frac{1}{2} \) as \( x \to 0 \).
limits