Let , where denotes the greatest integral function then which is not…

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let f(x)=cos⁡π(∣x∣+[x])f(x) = \cos \pi(|x| + [x]), where [⋅][\cdot] denotes the greatest integral function then which is not true? (a) Continuous at x=1/2x = 1/2 (b) Continuous at x=0x = 0 (c) Differentiable in (−1,0)(-1, 0) (d) Differentiable in (0,1)(0, 1)

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