Question

$\underset{x\to 1}{lim}\{1-x+[x+1]+[1-x\left]\right\}$ , where $\left[x\right]$ denotes greatest integer function, is

• A. $0$
• B. $1$
• C. $-1$
• D. $2$

Answer 1

Answer: (B)

$1$

Substitute $x=1+t$
L.H.S ${lim}_{t\to o^{-}}(-t+[2+t]+[-t\left]\right)$
$=0+1+0=1$
R.H.S ${lim}_{t\to o^{+}}(-t+[2+t]+[-t\left]\right)$
$=0+2-1=1$
L.H.S$=$R.H.S