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The function f(x)=(sin(pi[x-pi]))/(4+[x]...

The function `f(x)=(sin(pi[x-pi]))/(4+[x]^2)` , where `[]` denotes the greatest integer function, is continuous as well as differentiable for all `x in R`
(b) continuous for all `x` but not differentiable at some `x`
(c) differentiable for all `x` but not continuous at some `x`
. (d) none of these

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As,` [x]^2+4!=0`
Also `[x−pi]` is always an integer
So,`p[x−pi]` is of the form `kpi` (k is any integer)
and hence f(x) is identically the zero function for all x.
So it is a constant function.
Thus it is differentiable for all x
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