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The function f(x)=(tan{pi[x-(pi)/(2)]})/...

The function `f(x)=(tan{pi[x-(pi)/(2)]})/(2+[x]^(2))` , where [x] denotes the greatest integer `lex`, is

A

continous for all values of x

B

discontinuous at `x=(pi)/(2)`

C

not differentiable for some values of x

D

discontinuous at x = -2

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