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lim-x-0-nsinx-x-ntanx-x-where-denotes-the-greatest-integer-function-and-n-I-0-




Question Number 175762 by infinityaction last updated on 06/Sep/22
  lim_(xā†’0) ([((nsinx )/x)]+[((ntanx )/x)]) , where [:] denotes    the greatest integer function  and     nāˆˆIāˆ’{0}
$$\:\:\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{\mathrm{lim}}}\left(\left[\frac{\boldsymbol{\mathrm{nsinx}}\:}{\boldsymbol{\mathrm{x}}}\right]+\left[\frac{\boldsymbol{\mathrm{ntanx}}\:}{\boldsymbol{\mathrm{x}}}\right]\right)\:,\:\boldsymbol{\mathrm{where}}\:\left[:\right]\:\boldsymbol{\mathrm{denotes}} \\ $$$$\:\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{greatest}}\:\boldsymbol{\mathrm{integer}}\:\boldsymbol{\mathrm{function}}\:\:\boldsymbol{\mathrm{and}}\: \\ $$$$\:\:\boldsymbol{\mathrm{n}}\in\mathbb{I}āˆ’\left\{\mathrm{0}\right\} \\ $$

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