Question Number 96314 by Ar Brandon last updated on 31/May/20
![a\ Let E(x) denote the whole number part of the real number x, determine E(x^x ) and E(x^x^x ) for x∈]0,1[ b\ Calculate lim_(x→0) E(x^x^x )](https://www.tinkutara.com/question/Q96314.png)
$$\mathfrak{a}\backslash\:\mathcal{L}\mathfrak{et}\:\boldsymbol{\mathrm{E}}\left(\mathfrak{x}\right)\:\boldsymbol{\mathrm{d}}\mathfrak{enote}\:\mathfrak{the}\:\mathfrak{whole}\:\mathfrak{number}\:\mathfrak{part}\:\mathfrak{of}\:\mathfrak{the}\:\mathfrak{real} \\ $$$$\left.\mathfrak{number}\:\mathfrak{x},\:\boldsymbol{\mathrm{d}}\mathfrak{etermine}\:\boldsymbol{\mathrm{E}}\left(\mathfrak{x}^{\mathfrak{x}} \right)\:\mathfrak{an}\boldsymbol{\mathrm{d}}\:\boldsymbol{\mathrm{E}}\left(\mathfrak{x}^{\mathfrak{x}^{\mathfrak{x}} } \right)\:\mathfrak{for}\:\mathfrak{x}\in\right]\mathrm{0},\mathrm{1}\left[\right. \\ $$$$\mathfrak{b}\backslash\:\mathcal{C}\mathfrak{alculate}\:\underset{\mathfrak{x}\rightarrow\mathrm{0}} {\mathfrak{lim}}\boldsymbol{\mathrm{E}}\left(\mathfrak{x}^{\mathfrak{x}^{\mathfrak{x}} } \right) \\ $$