The value of k for which f(x) = (1 − cos(2x))/x² (for x ≠ 0) and f(0) = k is continuous at x = 0 is:

The value of k for which f(x) = (1 − cos(2x))/x² (for x ≠ 0) and f(0) = k is continuous at x = 0 is:

• A. 0
• B. 1
• C. 2
• D. 4

Answer: C) 2

Explanation: Using trigonometric identity, 1 − cos(2x) = 2sin²x. The limit is lim(x→0) (2sin²x)/x² = 2 × (lim(x→0) sin x / x)² = 2 × 1² = 2. So, k = 2.