Source Latex
du cours de mathématiques
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\usepackage{longtable}
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\usepackage{hyperref}
\hypersetup{
pdfauthor={Yoann Morel},
pdfsubject={Math�matiques: Logique},
pdftitle={Logique},
pdfkeywords={Math�matiques, TS, terminale, S,
logique, r�visions,
}
}
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% Raccourcis diverses:
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\def\Cf{\mathcal{C}_f}
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\ul{D�monstration:} #1%
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\renewcommand\thesection{\Roman{section}\ \ -}
\renewcommand\thesubsection{\arabic{subsection})}
% Bandeau en bas de page
\newcommand{\TITLE}{Logique}
\author{Y. Morel}
\date{}
\usepackage{fancyhdr}
\usepackage{lastpage}
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\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0.1pt}
\lhead{}\chead{}\rhead{}
\lfoot{Y. Morel \url{https://xymaths.fr/Lycee/TS/}}
\rfoot{\TITLE\ - \thepage/\pageref{LastPage}}
%\cfoot{\TITLE\ - \ $T^{\mbox{\scriptsize{ale}}}S$}
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%% Environnement Prog...
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\newlength{\hgn}\newlength{\hgnp}
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% avec un argument optionnel: le titre:
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\enmp
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% sans argument optionnel: le titre est alors "Programme Python"
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\par%\vspd%
\bgmp{\linewidth}
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\psframebox[fillstyle=solid,fillcolor=graypc]{
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\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
%\thispagestyle{empty}
\vspace*{-0.5cm}
\hfill{\LARGE \bf \TITLE}
\hfill $T^{\text{\scriptsize{ale}}}S$
\vspq
Compl�ter avec $\Rightarrow$, $\Leftarrow$, $\iff$ \dots\
ou/et avec "si", "alors", "si et seulement si" \dots
\vsp
Indiquer de plus, lorsque c'est possible, le nom de la propri�t� ou du
th�or�me correspondant.
\vspq
%\setlength{\extrarowheight}{0.8cm}
\renewcommand{\arraystretch}{2}
\begin{tabular}{|p{2cm}|p{6.5cm}|p{2cm}|p{5cm}|}\hline
&$(u_n)$ est une suite telle que
$u_0\leqslant u_1$, $u_1\leqslant u_2$
et $u_2\leqslant u_3$
&&$(u_n)$ est croissante
\\\hline
&$\dsp\lim_{x\to 2} f(x)=+\infty$
&&$x=2$ est asymptote � $\Cf$
\\\hline
&$\forall x\in\R^*$, $f(x)=3x^2-\dfrac1x$
&&$\forall x\in\R^*$, $f'(x)=6x+\dfrac{1}{x^2}$
\\\hline
&$x^2>1$
&&$x>1$
\\\hline
&$(u_n)$ est croissante et,
pour $n\in\N$, $u_n<3$
&& $(u_n)$ converge vers $3$
\\\hline
&$(u_n)$ telle que $u_0\!=\!8$ et $u_{n+1}\!=\!3u_n+2$
&&$(u_n)$ converge vers $-1$
\\\hline
&$(u_n)$ croissante et converge vers $l\!\in\!\R$
&&Pour tout $n\in\N$, $u_n\leqslant l$
\\\hline
&Pour tout $x\in\R$, $f'(x)\geqslant 0$
&&$f$ croissante sur $[3;8]$
\\\hline
&$(x+2)(x^2-3x+2)=0$
&&
$\rput(0.5,0.1){\text{ou}}\la\bgar{ll}x+2=0 \\[0.3cm] x^2-3x+2=0 \enar\right.$
\\\hline
&$\forall x\in[0;1], f(x)\leqslant g(x)$
&&
$\dsp\int_0^1 f(x)\,dx\leqslant \int_0^1 g(x)\,dx$
\\\hline
& $f$ continue telle que $f(3)=-1$ et $f(8)=6$
&& Il existe $\alpha\in]3;8[$ tel que $f(\alpha)=0$
\\\hline
& $f$ continue et strictement croissante sur $[0;1]$,
avec $f(0)=-2$ et $f(1)=3$
&& Il existe un unique $\alpha\in]0;1[$ tel que
$f(\alpha)=0$
\\\hline
& %\bgmp{5cm}
\mbox{\!Pour tout $x\!>\!10$, %\\
$g(x)\leqslant f(x)\leqslant h(x)$}
et
$\dsp\lim_{x\to+\infty} g(x)=\lim_{x\to+\infty} h(x)=3$
%\enmp
&&$\dsp\lim_{x\to+\infty} f(x)=3$
\\\hline
\end{tabular}
\begin{tabular}{|p{2cm}|p{6.5cm}|p{2cm}|p{5cm}|}\hline
&$\cos\tht=\dfrac{-\sqrt{2}}{2}$
&&
$\tht=\dfrac{3\pi}{4}$
\\\hline
&$ax^2+bx+c=2x^2+3x-2$
&& $a=2$, $b=3$, $c=-2$
\\\hline
&$f$ continue sur $[a;b]$
&& $f$ d�rivable sur $[a;b]$
\\\hline
&$f$ positive sur $[a;b]$
&& La fonction $F$ qui est une primitive de $f$ sur $[a;b]$ est
croissante
\\\hline
& $P(A\cap B)=P(A)\tm P(B)$
&& $A$ et $B$ sont ind�pendants
\\\hline
& $P(A)+P(B)=1$
&& $A=\overline{B}$
\\\hline
&$\dsp\int_0^{10} f(x)\,dx =1$
&&$f$ est une fonction densit� de probabilit� sur $[0;10]$
\\\hline
&La v.a. $X$ suit la loi $\mathcal{N}(\mu;\sigma^2)$
&&La v.a. $Y=\dfrac{X-\mu}{\sigma}$ suit la loi
$\mathcal{N}(0;1)$.
\\\hline
&$X$ suit la loi uniforme sur $[-2;8]$
&&$E(X)=3$
\\\hline
\end{tabular}
\end{document}
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