Question

If lim x _{x → 0} [4/x]  = A then the value of x at which f(x) = [x²] sinπx is discontinuous (where [.] denotes greatest integer function)

(1) √(A + 1)

(2) √(A + 21)

(3) √A

(4) √(A + 5)

Answer 1

Answer is (1)

check when

(A) x = √A + 1 ⇒ x = √5 ⇒ discontinuous

(B) x = √A + 21 ⇒ x = 5 ⇒  continuous

(C) x = √A ⇒ x = 2 ⇒ continuous

(D) x = √A + 5 ⇒ x = 3 ⇒ continuous