Question

The values of A and B such that the function f(x) = {(-2sinx, x ≤ -   π/2), (Asinx + B, - π/2 < x < π/2), (cosx, x ≥ π/2) is continuous every where are

(A) A = 0, B = 1

(B) A = 1, B = 1

(C) A = -1, B = 1

(D) A = -1, B = 0

Answer 1

Answer is (C) A = -1, B = 1

For continuity at all x ∈ R, we must have

From Eqs. (1) and (2), we get A = -1 and B = 1.