If f(x)=|x-1|-[x],w h e r e[x] is the gr...

If `f(x)=|x-1|-[x],w h e r e[x]` is the greatest integer less then or equal to `x` , then `f(1+0)-1,f(1-0)=0` `f(1+0)=0=f(1-0)` `("lim")_(xvec1)f(x)e xi s t s` `("lim")_(xvec1)f(x)doe snote xi s t`

`underset(xto0)lim[f(x)]=0`

`underset(xto0)lim[f(x)]=1`

`underset(xto0)lim[(f(x))/(x)]` does not exist

`underset(xto0)lim[(f(x))/(x)]` exists

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The correct Answer is:

A, D

`f(1+0)=underset(hto0)lim(|1+h-1|-[1+h])=underset(hto0)lim(h-1)=-1`
`f(1-0)=underset(hto0)lim(|1-h-1|-[1-h])=underset(hto0)lim(h-0)=0`

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