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 `el x`, is

A

continuous 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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The correct Answer is:

A

`:. [x-(pi)/(2)]` is always an integer and `tan k pi (k in I)` is always zero.
`:.f(x)= 0 AA x in R`
`:.f(x)` is continuous for all values of x.

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