If $f\left(x\right)=\left\{\begin{array}{ll}\frac{e^{\left[x\right]+\left|x\right|}-1}{\left[x\right]+\left|x\right|}& :x\ne 0\\ -1& :x=0\end{array}\right.$ (where $\left[.\right]$ denotes the greatest integer function), then

• A

  $f\left(x\right)$ is continuous at $x=0$
• B

  $\underset{x\to 0^{+}}{\mathrm{l}\mathrm{i}\mathrm{m}}f\left(x\right)=-1$
• C

  $\underset{x\to 0^{-}}{\mathrm{l}\mathrm{i}\mathrm{m}}f\left(x\right)=1$
• Correct answer
  D

  $\underset{x\to 0^{+}}{\mathrm{l}\mathrm{i}\mathrm{m}}f\left(x\right)=1$

Hence, the correct answer is option: 'D'.