Question

If the function f(x) = {(1 + sin(π/2) x for - ∞ < x ≤ 1), (ax + b for 1 < x < 3), (6tan(xπ/12) for 3≤ x < 6) is continuous in the interval (- ∞, 6), then the value of a and b are respectively ­

(A) 0, 2 

(B) 1, 1 

(C) 2, 0

 (D) 2, 1

Answer 1

Answer is (C) 2, 0

Obviously the function f(x) is continuous at x = 1 and 3. Therefore lim_(x →1⁺) f(x) = f(1)

⇒ a + b = 2  ....(1)

and  lim_{(x → 3^-)} f(x) = f(3)

⇒ 3a + b = 6  .....(2)

Solving (1) and (2), we get a = 2, b = 0.