Question

Solve:

${lim}_{x\to -1}(\left[x\right]+\left|x\right|)$ (where [.] denotes the greatest integer function)

• A. $0$
• B. $1$
• C. Does not exist
• D. None of these

Answer 1

The correct option is C Does not exist

$li{m}_{x\to -1}\left(\right[x]+|x|)$

LHD

$li{m}_{x\to -1^{-}}=-1-x=0$

RHD

$li{m}_{x\to -1^{+}}=-2-x=-1$

LHD $\ne$ RHD

limit does not exist

(c) is correct.