Question

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

• A. $0$
• B. $1$
• C. $-1$
• D. $2$

Answer 1

The correct option is C $-1$

We have,

${lim}_{x\to 1}(1-x+[x-1]+[1-x])$

$={lim}_{x\to 1}(1-x+\left[x\right]-1+[-x]+1)\therefore [t+k]=\left[t\right]+kifkisan\mathrm{int}izer$

$={lim}_{x\to 1}(-x+\left[x\right]+[-x]+1)$

$={lim}_{x\to 1}(-x-1+1)\therefore \left[x\right]+[-x]=-1$

$={lim}_{x\to 1}(-x)$

$=-1$