Question

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

• A. is $0$
• B. is $1$
• C. does not exist
• D. none of these

Answer 1

Answer: (C)

does not exist

${lim}_{x\to -1^{-}}\{\left[x\right]+\left|x\right|\}=-2+1=-1{lim}_{x\to -1^{+}}\{\left[x\right]+\left|x\right|\}=-1+1=0$