State the continuity of the function at the following points:

MATHEMATICS · Multi-part · AoPS · Mathematics · Special Functions · Special Functions

Problem

State the continuity of the function f(x)=⌊x⌋−⌊x−12⌋f(x)=\lfloor x\rfloor-\lfloor x-\tfrac12\rfloor at the following points: (i) x=1x=1 (ii) x=32x=\dfrac32

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