Question

Let [t] denote the greatest integer ≤ t and lim_(x→0) x[4/x] = A. Then the function, f(x) = [x²]sin(πx) is discontinuous, when x is equal to:

(1) √(A + 5)

(2) √(A + 1)

(3) √A

(4) √(A + 21)

Answer 1

Answer is (2) √(A + 1)

In option 1, 3, 4 values are integer and Integral Multiple of ∈ in sine is always zero.

∴ f(x) is disc. at √(A + 1)

Answer 2

Answer is (2) √(A + 1)

ƒ(x) = [x²]sin(πx) will be discontinuous at non integers

∴ x = √(A + 1) i.e √5