A) Continuous at \[x=0\]
B) Continuous in \[(-1,0)\]
C) Differentiable in (?1,1)
D) All the above
Correct Answer: D
Solution :
Here, when \[-1\le x\le 1,\,\,0\le x\sin \pi x<1\] \[\Rightarrow \,\,f(x)=[x\,\sin \pi x]=0\]for \[-1\le x\le 1,\,\] i.e., \[f(x)\] is constant function (equal to zero) in \[[-1,\,\,1].\] \[\Rightarrow \,\,f(x)\] is differentiable in \[(-1,\,\,1)\].
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