Question Number 175762 by infinityaction last updated on 06/Sep/22
![lim_(x→0) ([((nsinx )/x)]+[((ntanx )/x)]) , where [:] denotes the greatest integer function and n∈I−{0}](Q175762.png)
$$\:\:\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{\mathrm{lim}}}\left(\left[\frac{\boldsymbol{\mathrm{nsinx}}\:}{\boldsymbol{\mathrm{x}}}\right]+\left[\frac{\boldsymbol{\mathrm{ntanx}}\:}{\boldsymbol{\mathrm{x}}}\right]\right)\:,\:\boldsymbol{\mathrm{where}}\:\left[:\right]\:\boldsymbol{\mathrm{denotes}} \\ $$$$\:\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{greatest}}\:\boldsymbol{\mathrm{integer}}\:\boldsymbol{\mathrm{function}}\:\:\boldsymbol{\mathrm{and}}\: \\ $$$$\:\:\boldsymbol{\mathrm{n}}\in\mathbb{I}−\left\{\mathrm{0}\right\} \\ $$