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If f(x)=|x-1|-[x], \where\ [x] is the gr...

If `f(x)=|x-1|-[x], \where\ [x]` is the greatest integer less then or equal to `x` , then
(A)`f(1+0)=-1,f(1-0)=0`
(B) `f(1+0)=0=f(1-0)`
(C) `("lim")_(x to1)f(x)` exists
(D) `("lim")_(x to1)f(x) `does not exist

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

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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