Question

Consider f(x) = [(2(sinx - sin³x) + |sinx - sin³x|)/(2(sinx - sin³x) - |sinx - sin³x|)], x ≠ π/2 for x ∈ (0, π) f(π/2) = 3 where [] denotes the greatest integer function then,

(A) f is continuous & differentiable at x = π/2

(B) f is continuous but not differentiable at x = π/2

(C) f is neither continuous nor differentiable at x = π/2

(D) none of these 

Answer 1

Answer is (A) f is continuous & differentiable at x = π/2

In the immediate neighborhood of x = π/2, sinx > sin³x ⇒ |sinx - sin³x| = sinx - sin³x

Hence for x ≠ π/2,

Hence f is continuous and diff. at x = π/2