Let denote the greatest integer less than or equal to

MATHEMATICS · Multi correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let [x][x] denote the greatest integer less than or equal to xx. If f(x)=[xsin⁡πx]f(x)=[x\sin\pi x], then f(x)f(x) is: (1) Continuous at x=0x=0 (2) Continuous in (−1,0)(-1,0) (3) Differentiable at x=1x=1 (4) Differentiable in (−1,1)(-1,1)

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