حاصل $\underset{x\to {{۳}^{-}}}{\mathop{\lim }}\,\frac{\left[ x \right]-x}{\left| x \right|-۳}$ کدام است؟
$\underset{x\to {{3}^{-}}}{\mathop{\lim }}\,\frac{\left[ x \right]-x}{\left| x \right|-3}=\frac{\left[ {{3}^{-}} \right]-3}{\left| {{3}^{-}} \right|-3}=\frac{2-3}{{{3}^{-}}-3}=\frac{-1}{{{0}^{+}}}=+\infty $