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:

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:

The value of limx → ∞ (1 + 23x)x is: