If f(x) = { (sin² ax)/(tan bx), x ≠ 0; k, x = 0 } is continuous at x = 0, then k equals:

If f(x) = { (sin² ax)/(tan bx), x ≠ 0; k, x = 0 } is continuous at x = 0, then k equals:

• A. a²/b
• B. b/a²
• C. a/b²
• D. 0

Answer: A) a²/b

Explanation: lim(x→0) sin² ax / tan bx = lim(x→0) [(sin ax/ax)² × a² x²] / [(tan bx/bx) × bx] = (1 × a² x²)/(1 × bx) = a² x/b → 0. For continuity, k = a²/b.