f(x) = x +[x], x in Z, is f(x) continuous at x =0 ?

How to interpret [x], the books says in the answer section that R.H limit is 0 and L.H limit is -1.

Can anyone tell me how this was solved.

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- Dec 10th 2010, 01:00 AMkumaran5555Continuity and Differentiability
f(x) = x +[x], x in Z, is f(x) continuous at x =0 ?

How to interpret [x], the books says in the answer section that R.H limit is 0 and L.H limit is -1.

Can anyone tell me how this was solved. - Dec 10th 2010, 01:32 AMFernandoRevilla
Use:

$\displaystyle [x]=\begin{Bmatrix} -1 & \mbox{ if }& -1<x<0\\\;\;0 & \mbox{if}&\;\; 0\leq x <1\end{matrix}$

Fernando Revilla