WBJEE · Maths · Continuity and Differentiability
Let \(f(x)=\left[x^2\right] \sin \pi x, x > 0\). Then
- A \(f\) is discontinuous everywhere.
- B \(f\) is continuous everywhere.
- C \(f\) is continuous at only those points which are perfect squares.
- D None of these
Answer & Solution
Correct Answer
(D) None of these
Step-by-step Solution
Detailed explanation
Hint: \(\underset{\downarrow \atop \large \text{discontinuous}}{\left[x^2\right]} \sin \pi x\) at all points where \(x^2\) is integer If \(x^2\) is integer and \(x\) is also integer then \(f(x)\) will be continuous, but if \(x^2\) is integer and \(x\) is not integer then…
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