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The function $\mathrm{f}(x)=[x] \cdot \cos \left(\frac{2 x-1}{2}\right) \pi$, where $[\cdot]$ denotes the greatest integer function, is discontinuous at
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all integer points.
Greatest integer function is discontinuous on integer values.
$\therefore \quad \mathrm{f}(x)$ is discontinuous at all integer points.
$\therefore \quad \mathrm{f}(x)$ is discontinuous at all integer points.
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