Draw the graph and find the points of di...

Draw the graph and find the points of discontinuity `f(x) = [2cos x]` , `x in [0, 2pi]` . ([.] represents the greatest integer function.)

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From the graph of `y=2cosx,` the graph of `y=[2cosx]` can be drawn as shown in the following figure.

Clearly from the graph, f(x) is discontinuous at
`x=0andx=(pi)/(3),(2pi)/(3),(4pi)/(3),(5pi)/(3)`

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