Let [t] denote the greatest integer \leq t \textrm{ } and \textrm{ } \underset{x \rightarrow 0}{lim} x \left[\right. \frac{4}{x} \left]\right. = A Then the function, f(x) = [x2] sin(πx) is discontinuous, when x is equal to :

Engineering

Mathematics

Types of Discontinuities

Question

Let [t] denote the greatest integer $\leq t and \lim_{x \to 0} x [\frac{4}{x}] = A$ Then the function, f(x) = [x²] sin(πx) is discontinuous, when x is equal to :

$\sqrt{A + 1}$

$\sqrt{A + 5}$

$\sqrt{A + 21}$

$\sqrt{A}$

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$\lim_{x \to 0} x (\frac{4}{x} - {\frac{4}{x}}) = A \Rightarrow \lim_{x \to 0} 4 - x {\frac{4}{x}} = A \Rightarrow 4 - 0 = A$

check when

(A) $x = \sqrt{A + 1} \Rightarrow x = \sqrt{5} \Rightarrow discontinuous$

(B) $x = \sqrt{A + 21} \Rightarrow x = 5 \Rightarrow continuous$

(D) $x = \sqrt{A + 5} \Rightarrow x = 3 \Rightarrow continuous$