Revision as of 22:12, 31 May 2024 by Bot (Created page with "<div class="d-none"><math> \newcommand{\indexmark}[1]{#1\markboth{#1}{#1}} \newcommand{\red}[1]{\textcolor{red}{#1}} \newcommand{\NOTE}[1]{$^{\textcolor{red}\clubsuit}$\marginpar{\setstretch{0.5}$^{\scriptscriptstyle\textcolor{red}\clubsuit}$\textcolor{blue}{\bf\tiny #1}}} \newcommand\xoverline[2][0.75]{% \sbox{\myboxA}{$\m@th#2$}% \setbox\myboxB\null% Phantom box \ht\myboxB=\ht\myboxA% \dp\myboxB=\dp\myboxA% \wd\myboxB=#1\wd\myboxA% Scale phantom...")
BBy Bot
May 31'24
Exercise
[math]
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\sbox{\myboxA}{$\m@th#2$}%
\setbox\myboxB\null% Phantom box
\ht\myboxB=\ht\myboxA%
\dp\myboxB=\dp\myboxA%
\wd\myboxB=#1\wd\myboxA% Scale phantom
\sbox\myboxB{$\m@th\overline{\copy\myboxB}$}% Overlined phantom
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\fi}
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\label{Pa0} Show that in Lemma indeed [math]a_0\in(1,\sqrt{5}-1)[/math] holds. \smallskip { \small Hint: Establish first that [math]\exp(x)\leqslant 1+x+x^2/2[/math] holds for [math]x\leqslant0[/math]. }