• # question_answer $\underset{x\,\to \,0}{\mathop{\text{Limit}}}\,\,\,\frac{{{\log }_{e}}[x]}{x}$ where [ ] denotes the greatest integer function is: A) 0          B) 1 C) $-1$ D) non-existent

 $L=\underset{x\,\to \,\infty }{\mathop{Limit}}\,\frac{\ell n\,[x]}{x}$ $\underset{x\,\to \,\infty }{\mathop{Limit}}\,\frac{\ell n\,[x]}{x}\le L\le \underset{x\,\to \,\infty }{\mathop{Limit}}\,\frac{\ell n\,x}{x}$ $\underset{x\,\to \,\infty }{\mathop{Limit}}\,\left( \frac{1}{x-1}\le L\le \frac{1}{x} \right)$$\Rightarrow$      $0\le L\le 0$$\Rightarrow$            $L=0$