Let [t] denote the greatest integer less than or equal to t. If the function f(x) = b2 sin(π/2 [π/2 (cos x + sin x)]), for x 0 f(x) = a, for x = 0 is continuous at x = 0, then find a2 + b2.

If the function f(x) defined as: f(x) = sin(3x)tan(2x) for x 0 is continuous at x = 0, where α and β are coprime, then the value of α + 3β is equal to:

The value of limx → 0 (ax + bx2)1/x is:

If the function f(x) defined as: f(x) = k cos xπ - 2x, for x ≠ π2 f(x) = 3, for x = π2 is continuous at x = π2, then k is equal to: