Let [t] denote the greatest integer $ \le $ t and $\mathop {\lim }\limits_{x \to 0} x\left[ {{4 \over x}} \right] = A$. Then the function, f(x) = [x2]sin($\pi $x) is discontinuous, when x is equal to :

Question

Let [t] denote the greatest integer $ \le $ t and $\mathop {\lim }\limits_{x \to 0} x\left[ {{4 \over x}} \right] = A$.
Then the function, f(x) = [x²]sin($\pi $x) is discontinuous, when x is equal to :

$\sqrt {A + 1} $

$\sqrt {A + 5} $

$\sqrt {A + 21} $

$\sqrt {A} $

Solution

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