find-lim-x-0-log-x-n-x-x-n-N-where-x-represents-greatest-integer-less-than-or-equal-to-x-

Question Number 141966 by gsk2684 last updated on 25/May/21

$${find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{log}\:{x}^{{n}} −\left[{x}\right]}{\left[{x}\right]},\:{n}\in{N}\:{where}\: \\ $$$$\left[{x}\right]\:{represents}\:{greatest}\:{integer}\:{less}\:{than}\:{or}\:{equal}\:{to}\:{x}. \\ $$

Commented by gsk2684 last updated on 25/May/21

$${solution}\:{please} \\ $$

Commented by mathmax by abdo last updated on 26/May/21

$$\mathrm{limit}\:\mathrm{give}\:\frac{−\infty}{\mathrm{0}}−\mathrm{1}\left(\:\mathrm{indetermined}\:\mathrm{form}\:\mathrm{and}\:\mathrm{0}\:\mathrm{here}\:\mathrm{is}\:\mathrm{not}\:\mathrm{0}^{+} \:\mathrm{or}\:\mathrm{0}^{−} \right) \\ $$

Commented by gsk2684 last updated on 26/May/21

$${fraction}\:{is}\:{split}\:{in}\:{to}\:{two}\:{terms}. \\ $$$${then}\:{i}\:{could}\:{not}\:{understand}\:{well}.\: \\ $$$${explain}\:{me}\:{in}\:{detailed}\:{proof}\:{sir}. \\ $$

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