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Find the period - [Iran Second Round 1984]

Source:

December 30, 2010
functiontrigonometryfloor functionlimitalgebra unsolvedalgebra

Problem Statement

Consider the function f(x)=sin⁡(π2⌊x⌋).f(x)= \sin \biggl( \frac{\pi}{2} \lfloor x \rfloor \biggr). Find the period of ff and sketch diagram of ff in one period. Also prove that lim⁡x→1f(x)\lim_{x \to 1} f(x) does not exist.
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