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Let f(x)={[x]x in I x-1x in I (where [...

Let `f(x)={[x]x in I x-1x in I` (where [.] denotes the greatest integer function) and `g(x)={sinx+cosx ,x<0 1,xgeq0` . Then for `f(g(x))a tx=0` `(lim)_(xvec0)f(g(x))` exists but not continuous Continuous but not differentiable at `x=0` Differentiable at `x=0` `(lim)_(xvec0)f(g(x))` does not exist `f(x)` is continuous but not differentiable

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