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$\hspace*{-0.3cm}%
\begin{tabular}
[c]{llll}%
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& $Cte$\dotfill%
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\ \ $

\vspace{-0.3cm}%
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$\star$ $f$ continue en $x_{0}$ ssi:$\vspace*{-0.35cm}$%
\[
\underset{x\rightarrow x_{0}}{\lim}f(x_{0})=f(x_{0})
\]
$\vspace*{-0.4cm}$

$\star$ $f$ d\'{e}rivable en $x_{0}$ et $f^{\prime}(x_{0})=\ell\vspace*{-0.3cm}$%
\begin{align*}
&  \Leftrightarrow\underset{x\rightarrow x_{0}}{\lim}\dfrac{f(x)-f(x_{0}%
)}{x-x_{0}}=\ell\in%
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\end{align*}
$\vspace*{-0.4cm}$

$\star$ $f$ {\small d\'{e}riv}$^{\text{{\tiny able}}}${\small en}
$x_{0}\overset{\nLeftarrow}{\Longrightarrow}f$ {\small cont}%
$^{\text{{\tiny inue}}}${\small en} $x_{0}$

$\star$ Si $f$ d\'{e}ribale en $x_{0}$ alors:

\begin{itemize}
\item[$\hspace*{0.2cm}$.] $T_{x_{0}}:y=f^{\prime}(x_{0})(x-x_{0}%
)+f(x_{0})\vspace*{0.15cm}$

\item[$\hspace*{0.2cm}$.] $\left\{
\begin{array}
[c]{c}%
f(x)=T_{x_{0}}(x)+\epsilon(x)\\
\text{avec }\underset{x\rightarrow x_{0}}{\lim}\epsilon(x)=0
\end{array}
\right.  $
\end{itemize}

%

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\begin{center}
\underline{\underline{\textbf{Pour} $a<b$}}\vspace*{-0.3cm}
\end{center}

$\star$ Si $f(x)\geq0$ sur $\left[  a;b\right]  $ alors $\int_{a}%
^{b}f(x)dx\geq0\vspace*{0.28cm}$

$\star$ Si $m\leq f(x)\leq M$ sur $\left[  a;b\right]  $ alors:\vspace
*{-0.2cm}%
\[
m(b-a)\leq\int_{a}^{b}f(x)dx\leq M(b-a)
\]
%

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\vspace*{0.3cm}

$\star$ $\int_{a}^{b}uv^{\prime}=\left[  uv\right]  _{a}^{b}-\int_{a}%
^{b}u^{\prime}v\vspace*{0.15cm}$

$\star$ Val moyenne: $\mu=\dfrac{1}{b-a}\int_{a}^{b}f(x)dx\vspace*{0.15cm}$

$\star$ Volume: $V=\int_{x_{1}}^{x_{2}}S(x)dx\vspace*{0.15cm}$

$\star$ V r\'{e}volution: $V=\int_{x_{1}}^{x_{2}}\pi\left[  f(x)\right]
^{2}dx$%

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$\star$ $y^{\prime}=ay\Leftrightarrow y=Cte\times e^{ax}\hspace*{1.96cm}\star$
$y^{\prime}=ay+b\Leftrightarrow y=Cte\times e^{ax}-\tfrac{b}{a}$%

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$\star$ $(D):x=a$ asymptote verticale \`{a} $C_{f}$ ssi $\underset
{x\rightarrow a}{\lim}f(x)=\infty$

$\star$ $(D):y=b$ asymptote horizontale \`{a} $C_{f}$ ssi $\underset
{x\rightarrow\infty}{\lim}f(x)=b$

$\star$ $(D):y=ax+b$ asymptote oblique \`{a} $C_{f}$ ssi $\underset
{x\rightarrow\infty}{\lim}[f(x)-(ax+b)]=0$

$\star$ $C_{g}$ courbe asymptote \`{a} $C_{f}$ ssi $\underset{x\rightarrow
\infty}{\lim}[f(x)-g(x)]=0\vspace*{-0.25cm}$

\hrulefill$\vspace*{-0.1cm}$

$\hspace*{\fill}$%
\begin{tabular}
[c]{ll}
& $\forall h$ tel que $a-h$ et $a+h$ dans $\mathcal{D}_{f}$\\
$\star$ $(D):x=a$ est axe de sym\'{e}trie de $C_{f}$ ssi: &
\multicolumn{1}{c}{$\dfrac{f(a-h)+f(a+h)}{2}=a$}\\
$\star$ $\Omega(a;b)$ est centre de sym\'{e}trie de $C_{f}$ ssi:%
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& \multicolumn{1}{c}{$\dfrac{f(a-h)+f(a+h)}{2}=b$}%
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$\hspace*{\fill}$%

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\begin{boxedminipage}[t]{14.4cm}%
%EndExpansion


$\star$ $\underset{x\rightarrow\infty}{\lim}Polyn\hat{o}me(x)=\underset
{x\rightarrow\infty}{\lim}${\small mon\^{o}me de plus haut degr\'{e}
}$=\underset{x\rightarrow\infty}{\lim}a_{p}x^{p}\quad\left(  p=\deg P\right)
\vspace*{0.1cm}$

$\star$ $\underset{x\rightarrow\infty}{\lim}\dfrac{Polyn\hat{o}me\_P(x)}%
{Polyn\hat{o}me\_Q(x)}=\underset{x\rightarrow\infty}{\lim}\dfrac
{\text{{\small mon\^{o}me de plus haut degr\'{e} de} }P}%
{\text{{\small mon\^{o}me de plus haut degr\'{e} de} }Q}=\underset
{x\rightarrow\infty}{\lim}\dfrac{a_{p}x^{p}}{b_{q}x^{q}}\vspace*{0.2cm}$

\hrulefill$\vspace*{-0.3cm}$%

%TCIMACRO{\TeXButton{BeginMulticols}{
%\begin{multicols}{3} }}%
%BeginExpansion
\begin{multicols}{3}
%EndExpansion
%

%TCIMACRO{\TeXButton{BeginEspaceLigne}{\renewcommand{\baselinestretch}%
%{1.30}\small\normalsize}}%
%BeginExpansion
\renewcommand{\baselinestretch}{1.30}\small\normalsize
%EndExpansion


$\star$ $x^{\tfrac{1}{n}}=\sqrt[n]{x}$

$\star$ $x^{\frac{1}{2}}=\sqrt{x}$

$\star$ $x^{\tfrac{p}{q}}=\sqrt[q]{x^{p}}$

$\star$ $x^{r}\times x^{r^{\prime}}=x^{r+r^{\prime}}$

$\star$ $\tfrac{x^{r}}{x^{r^{\prime}}}=x^{r-r^{\prime}}$

$\star$ $\left(  x^{r}\right)  ^{r^{\prime}}=x^{rr^{\prime}}$%

%TCIMACRO{\TeXButton{endEspaceLigne}{
%\renewcommand{\baselinestretch}{1}\small\normalsize}}%
%BeginExpansion
\renewcommand{\baselinestretch}{1}\small\normalsize
%EndExpansion
%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion
$\vspace*{-0.69cm}$%

%TCIMACRO{\TeXButton{EndBoxe}{\end{boxedminipage}}}%
%BeginExpansion
\end{boxedminipage}%
%EndExpansion%
%TCIMACRO{\TeXButton{EMinipage}{\end{minipage}}}%
%BeginExpansion
\end{minipage}%
%EndExpansion
%

%TCIMACRO{\TeXButton{BMinipage}{\begin{minipage}[t]{8.2cm}}}%
%BeginExpansion
\begin{minipage}[t]{8.2cm}%
%EndExpansion
%

%TCIMACRO{\TeXButton{beginBox}{\setlength{\fboxrule}{1pt}
%\begin{boxedminipage}[t]{8.2cm}}}%
%BeginExpansion
\setlength{\fboxrule}{1pt}
\begin{boxedminipage}[t]{8.2cm}%
%EndExpansion


$\star$ {\small Droite}$\left(  \text{{\small Point}}(x_{0};y_{0}%
;z_{0}),\overrightarrow{directeur}(a;b;c)\right)  :\vspace*{-0.35cm}$%
\[
\left\{
\begin{array}
[c]{c}%
x=x_{0}+at\\
y=y_{0}+bt\\
z=z_{0}+ct
\end{array}
\right.  t\in%
%TCIMACRO{\TeXButton{R}{\mathbb{R}}}%
%BeginExpansion
\mathbb{R}%
%EndExpansion
\]
$\vspace*{-0.3cm}$

$\star$ {\small Plan}$\left(  \text{{\small Point}}(x_{0};y_{0};z_{0}%
),\overrightarrow{normal}(a;b;c)\right)  :\vspace*{-0.35cm}$%
\begin{align*}
ax+by+cz+d  &  =0\\
\text{avec }d  &  =-ax_{0}-by_{0}-cz_{0}%
\end{align*}
%

%TCIMACRO{\TeXButton{EndBoxe}{\end{boxedminipage}}}%
%BeginExpansion
\end{boxedminipage}%
%EndExpansion
%

%TCIMACRO{\TeXButton{beginBox}{\setlength{\fboxrule}{1pt}
%\begin{boxedminipage}[t]{8.2cm}}}%
%BeginExpansion
\setlength{\fboxrule}{1pt}
\begin{boxedminipage}[t]{8.2cm}%
%EndExpansion
$\vspace*{-0.1cm}$

$\star\overrightarrow{u}\cdot\overrightarrow{v}\hspace*{-0.05cm}%
\begin{array}
[t]{l}%
=\tfrac{1}{2}\left(  \left\Vert \overrightarrow{u}+\overrightarrow
{v}\right\Vert ^{2}-\left\Vert \overrightarrow{u}\right\Vert ^{2}-\left\Vert
\overrightarrow{v}\right\Vert ^{2}\right)
%TCIMACRO{\TeXButton{Ait�}{{\setlength{\fboxrule}{0pt}
%\setlength{\fboxsep}{0pt}
%\fbox{\rule[-3mm]{0pt}{0mm}}}}}%
%BeginExpansion
{\setlength{\fboxrule}{0pt}
\setlength{\fboxsep}{0pt}
\fbox{\rule[-3mm]{0pt}{0mm}}}%
%EndExpansion
\\
=\left\Vert \overrightarrow{u}\right\Vert \left\Vert \overrightarrow
{v}\right\Vert \cos\left(  \overrightarrow{u};\overrightarrow{v}\right)
\end{array}
$

$\star$Dans un rep\`{e}re orthonormal direct:$\vspace*{-0.4cm}$%
\[
\overrightarrow{u}\cdot\overrightarrow{v}=x_{u}x_{v}+y_{u}y_{v}+z_{u}z_{v}%
\]
$\vspace*{-0.7cm}$

$\star\overrightarrow{u}\cdot\overrightarrow{u}=\left\Vert \overrightarrow
{u}\right\Vert ^{2}\hspace*{\fill}\star\left\Vert t\overrightarrow
{u}\right\Vert =\left\vert t\right\vert \left\Vert \overrightarrow
{u}\right\Vert \hspace*{\fill}\vspace*{-0.2cm}$

\hrulefill%

%TCIMACRO{\TeXButton{BMinipage}{\begin{minipage}{2.64cm}}}%
%BeginExpansion
\begin{minipage}{2.64cm}%
%EndExpansion
%

%TCIMACRO{\TeXButton{BMinipage}{\begin{minipage}{4cm}}}%
%BeginExpansion
\begin{minipage}{4cm}%
%EndExpansion


$\star\overrightarrow{AB}\cdot\overrightarrow{AC}=\overrightarrow{AB}%
\cdot\overrightarrow{AC^{\prime}}$%

%TCIMACRO{\TeXButton{EMinipage}{\end{minipage}}}%
%BeginExpansion
\end{minipage}%
%EndExpansion
$\vspace*{0.2cm}$

$\star\overrightarrow{AB}\cdot\overrightarrow{AE}=0\vspace*{0.2cm}$

$\star\overrightarrow{ME}\cdot\overrightarrow{AB}=0\vspace*{0.2cm}$

$\star\overrightarrow{AB}\cdot\overrightarrow{AD}<0\vspace*{0.2cm}$%

%TCIMACRO{\TeXButton{EMinipage}{\end{minipage}}}%
%BeginExpansion
\end{minipage}%
%EndExpansion
$\hspace*{\fill}$%
%TCIMACRO{\TeXButton{BMinipage}{\begin{minipage}{5.56cm}}}%
%BeginExpansion
\begin{minipage}{5.56cm}%
%EndExpansion
%

%TCIMACRO{\FRAME{itbpF}{2.1071in}{1.1366in}{0in}{}{}{Include/sca.eps}%
%{\special{ language "Scientific Word";  type "GRAPHIC";
%maintain-aspect-ratio TRUE;  display "USEDEF";  valid_file "F";
%width 2.1071in;  height 1.1366in;  depth 0in;  original-width 1.985in;
%original-height 1.0585in;  cropleft "0";  croptop "1";  cropright "1";
%cropbottom "0";  filename 'Include/sca.eps';file-properties "XNPEU";}}}%
%BeginExpansion
{\includegraphics[
height=1.1366in,
width=2.1071in
]%
{Include/sca.eps}%
}%
%EndExpansion%
%TCIMACRO{\TeXButton{EMinipage}{\end{minipage}}}%
%BeginExpansion
\end{minipage}%
%EndExpansion


$\star\mathcal{P\perp Q}$ car $\left(  AB\right)  $ $\perp$ \`{a} 2 droites
s\'{e}cantes de $\mathcal{P}$

$\star\mathcal{P}=Plan(A,\overrightarrow{n})\Leftrightarrow\forall
M\in\mathcal{P},$ $\overrightarrow{AM}\cdot\overrightarrow{n}=0$

$\star(AB)\perp\mathcal{P}$ donc $\forall(d)\subset\mathcal{P},$
$(AB)\perp(d)$%

%TCIMACRO{\TeXButton{EndBoxe}{\end{boxedminipage}}}%
%BeginExpansion
\end{boxedminipage}%
%EndExpansion
%

%TCIMACRO{\TeXButton{EMinipage}{\end{minipage}}}%
%BeginExpansion
\end{minipage}%
%EndExpansion
$\hspace*{\fill}$%
%TCIMACRO{\TeXButton{BMinipage}{\begin{minipage}[t]{11.7cm}}}%
%BeginExpansion
\begin{minipage}[t]{11.7cm}%
%EndExpansion%
%TCIMACRO{\TeXButton{beginBox}{\setlength{\fboxrule}{1pt}
%\begin{boxedminipage}[t]{11.7cm}}}%
%BeginExpansion
\setlength{\fboxrule}{1pt}
\begin{boxedminipage}[t]{11.7cm}%
%EndExpansion


$\hspace*{-0.2cm}$%
\begin{tabular}
[c]{lll}%
$\star$ $\ln(ab)=\ln a+\ln b$ & $\star$ $\ln\dfrac{a}{b}=\ln a-\ln b$ &
$\star$ $\ln a^{r}\overset{a>0}{=}r\ln a$\\
$\star$ $e^{a+b}=e^{a}\times e^{b}$ & $\star$ $e^{a-b}=\dfrac{e^{a}}{e^{b}}$ &
$\star$ $\left(  e^{a}\right)  ^{r}=e^{ra}$\\
$\star$ $\ln e^{x}=x$ o\`{u} $x\in%
%TCIMACRO{\TeXButton{R}{\mathbb{R}}}%
%BeginExpansion
\mathbb{R}%
%EndExpansion
$ & $\star$ $e^{\ln x}=x$ o\`{u} $x\in%
%TCIMACRO{\TeXButton{R}{\mathbb{R}}}%
%BeginExpansion
\mathbb{R}%
%EndExpansion
^{\ast+}$ & $\star$ $\ln1=0$\\
$\star$ $\log x=\dfrac{1}{\ln10}\ln x$ & $\star$ $\log_{a}x=\dfrac{1}{\ln
a}\ln x$ & $\star$ $a^{x}\overset{a>0}{=}e^{x\ln a}$\\
\multicolumn{3}{c}{\frame{%
%TCIMACRO{\TeXButton{Ait�}{{\setlength{\fboxrule}{0pt}
%\setlength{\fboxsep}{0pt}
%\fbox{\rule[-2.5mm]{0pt}{6.5mm}}}}}%
%BeginExpansion
{\setlength{\fboxrule}{0pt}
\setlength{\fboxsep}{0pt}
\fbox{\rule[-2.5mm]{0pt}{6.5mm}}}%
%EndExpansion
$\ln a=b\overset{a>0}{\Leftrightarrow}a=e^{b}$%
%TCIMACRO{\TeXButton{Ait�}{{\setlength{\fboxrule}{0pt}
%\setlength{\fboxsep}{0pt}
%\fbox{\rule[-2.5mm]{0pt}{6.5mm}}}}}%
%BeginExpansion
{\setlength{\fboxrule}{0pt}
\setlength{\fboxsep}{0pt}
\fbox{\rule[-2.5mm]{0pt}{6.5mm}}}%
%EndExpansion
}%
%TCIMACRO{\TeXButton{Ait�}{{\setlength{\fboxrule}{0pt}
%\setlength{\fboxsep}{0pt}
%\fbox{\rule[9mm]{0pt}{0mm}}}}}%
%BeginExpansion
{\setlength{\fboxrule}{0pt}
\setlength{\fboxsep}{0pt}
\fbox{\rule[9mm]{0pt}{0mm}}}%
%EndExpansion
}%
\end{tabular}
\vspace*{-0.3cm}

$\hspace*{-0.2cm}$%
\begin{tabular}
[c]{lll}%
$\star$ $\underset{x\rightarrow+\infty}{\lim}\ln x=+\infty$ & $\star$
$\underset{x\rightarrow0^{+}}{\lim}\ln x=-\infty$ & $\star$ $\underset
{x\rightarrow0}{\lim}\dfrac{\ln(x+1)}{x}=1$\\
$\star$ $\underset{x\rightarrow+\infty}{\lim}e^{x}=+\infty$ & $\star$
$\underset{x\rightarrow-\infty}{\lim}e^{x}=0$ & $\star$ $\underset
{x\rightarrow0}{\lim}\dfrac{e^{x}-1}{x}=1$%
%TCIMACRO{\TeXButton{Ait�}{{\setlength{\fboxrule}{0pt}
%\setlength{\fboxsep}{0pt}
%\fbox{\rule[7.2mm]{0pt}{0mm}}}}}%
%BeginExpansion
{\setlength{\fboxrule}{0pt}
\setlength{\fboxsep}{0pt}
\fbox{\rule[7.2mm]{0pt}{0mm}}}%
%EndExpansion
\end{tabular}
\vspace*{-0.3cm}

\begin{center}
\underline{\underline{Pour $r>0$}}$\left\{
\begin{tabular}
[c]{lll}%
$\underset{x\rightarrow0^{+}}{\lim}x^{r}\ln x=0$ &  & $\underset
{x\rightarrow-\infty}{\lim}\left\vert x\right\vert ^{r}e^{x}=0$\\
$\underset{x\rightarrow+\infty}{\lim}\dfrac{\ln x}{x^{r}}=0$ &
%TCIMACRO{\TeXButton{Ait�}{{\setlength{\fboxrule}{0pt}
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%BeginExpansion
{\setlength{\fboxrule}{0pt}
\setlength{\fboxsep}{0pt}
\fbox{\rule[-4mm]{0pt}{0mm}}}%
%EndExpansion
& $\underset{x\rightarrow+\infty}{\lim}\dfrac{e^{x}}{x^{r}}=+\infty$%
\end{tabular}
\right\}  $
\end{center}

%

%TCIMACRO{\TeXButton{endEspaceLigne}{\renewcommand{\baselinestretch}{1}%
%\small\normalsize}}%
%BeginExpansion
\renewcommand{\baselinestretch}{1}\small\normalsize
%EndExpansion
%

%TCIMACRO{\TeXButton{EndBoxe}{\end{boxedminipage}}}%
%BeginExpansion
\end{boxedminipage}%
%EndExpansion
%

%TCIMACRO{\TeXButton{beginBox}{\setlength{\fboxrule}{1pt}
%\begin{boxedminipage}[t]{11.7cm}}}%
%BeginExpansion
\setlength{\fboxrule}{1pt}
\begin{boxedminipage}[t]{11.7cm}%
%EndExpansion


$\star$ $\left\{  G=bar\{(A_{i},\alpha_{i})\text{ }1\leq i\leq n\}\text{ et
}\sum\alpha_{i}\neq0\right\}  \Leftrightarrow\sum\alpha_{i}\overrightarrow
{GA_{i}}=\overrightarrow{0}$

$\Leftrightarrow\overrightarrow{OG}=\dfrac{\sum\alpha_{i}\overrightarrow
{OA_{i}}}{\sum\alpha_{i}}\Leftrightarrow\left(  \sum\alpha_{i}\right)
\overrightarrow{MG}=\sum\alpha_{i}\overrightarrow{MA_{i}},\quad\forall
M\in\mathcal{E}\vspace*{0.1cm}$

$\Leftrightarrow G=Bar\left\{  (G^{\prime},\sum_{i=1}^{p}\alpha_{i}%
);(A_{p+1},\alpha_{p+1});\cdots(A_{n},\alpha_{n})\right\}  $

$\hspace*{\fill}$o\`{u} $G^{\prime}=bar\{\left(  A_{i},\alpha_{i}\right)
;\cdots;\left(  A_{p},\alpha_{p}\right)  \}$ s'il existe$\hspace*{\fill
}\vspace*{0.12cm}$

$\star$ $M\in Plan(ABC)\Leftrightarrow M=bar\{(A,\alpha);(B,\beta
);(C,\gamma)\}$

$\hspace*{3.5cm}\Leftrightarrow$il existe $x,y\in%
%TCIMACRO{\TeXButton{R}{\mathbb{R}}}%
%BeginExpansion
\mathbb{R}%
%EndExpansion
$ tq $\overrightarrow{AM}=x\overrightarrow{AB}+y\overrightarrow{AC}$%

%TCIMACRO{\TeXButton{EndBoxe}{\end{boxedminipage}}}%
%BeginExpansion
\end{boxedminipage}%
%EndExpansion
%

%TCIMACRO{\TeXButton{EMinipage}{\end{minipage}}}%
%BeginExpansion
\end{minipage}%
%EndExpansion

\vfill
\begin{center}%
\scriptsize{Imprim� avec \LaTeXe}%
\end{center}
\newpage%

%TCIMACRO{\TeXButton{beginBox}{\setlength{\fboxrule}{1pt}
%\begin{boxedminipage}[t]{9.95cm}}}%
%BeginExpansion
\setlength{\fboxrule}{1pt}
\begin{boxedminipage}[t]{9.95cm}%
%EndExpansion


\begin{center}
\underline{Suite arithm\'{e}tique}\vspace*{-0.5cm}
\end{center}

%

%TCIMACRO{\TeXButton{BeginMulticols}{\begin{multicols}{2} }}%
%BeginExpansion
\begin{multicols}{2}
%EndExpansion


$\star$ $u_{n+1}=u_{n}+r$

$\star$ $u_{n}=u_{0}+nr$

$\star$ $u_{n}=u_{p}+(n-p)r$

$\star$ $u_{n}=\tfrac{1}{2}(u_{n-1}+u_{n+1})$%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion
$\vspace*{-0.75cm}$

$\star$ $\vspace*{-0.75cm}$%
\begin{align*}
S_{n}  &  =u_{p}+u_{p+1}+\cdots+u_{n}\quad\text{o\`{u} }(p\leq n)\\
&  =\dfrac{1}{2}(n-p+1)(u_{p}+u_{n})%
%TCIMACRO{\TeXButton{Ait�}{{\setlength{\fboxrule}{0pt}
%\setlength{\fboxsep}{0pt}
%\fbox{\rule[-3mm]{0pt}{8.8mm}}}}}%
%BeginExpansion
{\setlength{\fboxrule}{0pt}
\setlength{\fboxsep}{0pt}
\fbox{\rule[-3mm]{0pt}{8.8mm}}}%
%EndExpansion
\end{align*}
%

%TCIMACRO{\TeXButton{EndBoxe}{\end{boxedminipage}}}%
%BeginExpansion
\end{boxedminipage}%
%EndExpansion
\hfill%
%TCIMACRO{\TeXButton{beginBox}{\setlength{\fboxrule}{1pt}
%\begin{boxedminipage}[t]{9.95cm}}}%
%BeginExpansion
\setlength{\fboxrule}{1pt}
\begin{boxedminipage}[t]{9.95cm}%
%EndExpansion


\begin{center}
\underline{Suite g\'{e}om\'{e}trique}\vspace*{-0.5cm}
\end{center}

%

%TCIMACRO{\TeXButton{BeginMulticols}{\begin{multicols}{2} }}%
%BeginExpansion
\begin{multicols}{2}
%EndExpansion


$\star$ $u_{n+1}=qu_{n}$

$\star$ $u_{n}=u_{0}q^{n}$

$\star$ $u_{n}=u_{p}q^{(n-p)}$

$\star$ $\left\vert u_{n}\right\vert =\sqrt{u_{n-1}\times u_{n+1}}$%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion
$\vspace*{-0.75cm}$

$\star$ $\vspace*{-0.75cm}$%
\begin{align*}
S_{n} &  =u_{p}+u_{p+1}+\cdots+u_{n}\quad\text{o\`{u} }(p\leq n)\\
&  =u_{p}\times\dfrac{1-q^{n-p+1}}{1-q}%
\end{align*}
%

%TCIMACRO{\TeXButton{EndBoxe}{\end{boxedminipage}}}%
%BeginExpansion
\end{boxedminipage}%
%EndExpansion
%

%TCIMACRO{\TeXButton{beginBox}{\setlength{\fboxrule}{1pt}
%\begin{boxedminipage}[t]{19.98cm}}}%
%BeginExpansion
\setlength{\fboxrule}{1pt}
\begin{boxedminipage}[t]{19.98cm}%
%EndExpansion
%

%TCIMACRO{\TeXButton{BeginMulticols}{
%\setlength{\columnseprule}{.4pt}
%\begin{multicols}{2} }}%
%BeginExpansion
\setlength{\columnseprule}{.4pt}
\begin{multicols}{2}
%EndExpansion
%

%TCIMACRO{\TeXButton{BMinipage}{\begin{minipage}{10cm}}}%
%BeginExpansion
\begin{minipage}{10cm}%
%EndExpansion
\vspace*{0.3cm}%

%TCIMACRO{\TeXButton{BeginMulticols}{
%\setlength{\columnseprule}{0pt}
%\begin{multicols}{2} }}%
%BeginExpansion
\setlength{\columnseprule}{0pt}
\begin{multicols}{2}
%EndExpansion


$\star$ $\left\vert a\right\vert <1\Leftrightarrow\underset{n\rightarrow
+\infty}{\lim}a^{n}=0$

$\hspace*{-0.3cm}\star$ $\left\vert a\right\vert >1\Leftrightarrow
\underset{n\rightarrow+\infty}{\lim}a^{n}=\pm\infty$%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion
%

%TCIMACRO{\TeXButton{EMinipage}{\end{minipage}}}%
%BeginExpansion
\end{minipage}%
%EndExpansion


$\star$ $\left.
\begin{array}
[c]{c}%
f\text{ continue sur }%
%TCIMACRO{\TeXButton{R}{\mathbb{R}}}%
%BeginExpansion
\mathbb{R}%
%EndExpansion
\\
\underset{n\rightarrow+\infty}{\lim}u_{n}=\ell
\end{array}
\right\}  \overset{\nLeftarrow}{\Longrightarrow}\underset{n\rightarrow+\infty
}{\lim}f(u_{n})=f(\ell)$%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion
%

%TCIMACRO{\TeXButton{EndBoxe}{\end{boxedminipage}}}%
%BeginExpansion
\end{boxedminipage}%
%EndExpansion
%

%TCIMACRO{\TeXButton{beginBox}{\setlength{\fboxrule}{1pt}
%\begin{boxedminipage}[t]{19.98cm}}}%
%BeginExpansion
\setlength{\fboxrule}{1pt}
\begin{boxedminipage}[t]{19.98cm}%
%EndExpansion
%

%TCIMACRO{\TeXButton{BeginMulticols}{
%\setlength{\columnseprule}{.4pt}
%\begin{multicols}{3} }}%
%BeginExpansion
\setlength{\columnseprule}{.4pt}
\begin{multicols}{3}
%EndExpansion


$\star$ $x=\operatorname{Re}(z)=\tfrac{1}{2}(z+\overline{z})$

$\star$ $y=\operatorname{Im}(z)=\tfrac{1}{2i}(z-\overline{z})$

$\star$ $z\in%
%TCIMACRO{\TeXButton{R}{\mathbb{R}}}%
%BeginExpansion
\mathbb{R}%
%EndExpansion
\Leftrightarrow z=\overline{z}$

$\star$ $z\in%
%TCIMACRO{\TeXButton{R}{\mathbb{R}}}%
%BeginExpansion
\mathbb{R}%
%EndExpansion
^{\ast}\Leftrightarrow\arg(z)=k\pi$

$\star$ $z\in i%
%TCIMACRO{\TeXButton{R}{\mathbb{R}}}%
%BeginExpansion
\mathbb{R}%
%EndExpansion
\Leftrightarrow z=-\overline{z}$

$\star$ $z\in i%
%TCIMACRO{\TeXButton{R}{\mathbb{R}}}%
%BeginExpansion
\mathbb{R}%
%EndExpansion
^{\ast}\Leftrightarrow\arg(z)=k\tfrac{\pi}{2}$%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion
$\vspace*{-1cm}$

\hrulefill$\vspace*{-0.4cm}$%

%TCIMACRO{\TeXButton{BeginMulticols}{
%\setlength{\columnseprule}{0pt}
%\begin{multicols}{4} }}%
%BeginExpansion
\setlength{\columnseprule}{0pt}
\begin{multicols}{4}
%EndExpansion


$\star$ $\overline{z}=x-iy$

$\star$ $\overline{z+z^{\prime}}=\overline{z}+\overline{z^{\prime}}$

$\star$ $\overline{zz^{\prime}}=\overline{z}\times\overline{z^{\prime}}$

$\star$ $\overline{\left(  \tfrac{z}{z^{\prime}}\right)  }=\tfrac{\overline
{z}}{\overline{z^{\prime}}}$%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion
$\vspace*{-1cm}$

\hrulefill$\vspace*{-0.4cm}$%

%TCIMACRO{\TeXButton{BeginMulticols}{
%\setlength{\columnseprule}{.4pt}
%\begin{multicols}{2} }}%
%BeginExpansion
\setlength{\columnseprule}{.4pt}
\begin{multicols}{2}
%EndExpansion


$\star$ $\overrightarrow{MM^{\prime}}\left(  z^{\prime}-z\right)  $

$\star$ $\left\vert z\right\vert =\sqrt{z\overline{z}}=\sqrt{x^{2}+y^{2}}=OM$

$\star$ $\left\vert z^{\prime}-z\right\vert =MM^{\prime}$

$\star$ $\arg(z)=\left(  \overrightarrow{Ox},\overrightarrow{OM}\right)
+k2\pi$%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion
\vspace*{-0.6cm}

\hrulefill$\vspace*{-0.2cm}$

\begin{center}
$\left\vert z\right\vert =r$ et $\arg(z)=\alpha+k2\pi\overset{k\in%
%TCIMACRO{\TeXButton{Z}{\mathbb{Z}}}%
%BeginExpansion
\mathbb{Z}%
%EndExpansion
}{\Leftrightarrow}z=r(\cos\alpha+i\sin\alpha)\Leftrightarrow z=re^{i\alpha}%
$\vspace*{-0.35cm}
\end{center}

\hrulefill$\vspace*{-0.4cm}$%

%TCIMACRO{\TeXButton{BeginMulticols}{
%\setlength{\columnseprule}{.4pt}
%\begin{multicols}{3} }}%
%BeginExpansion
\setlength{\columnseprule}{.4pt}
\begin{multicols}{3}
%EndExpansion


$\star$ $\left\vert z\right\vert =0\Leftrightarrow z=0$

$\star$ $\left\vert z+z^{\prime}\right\vert \leq\left\vert z\right\vert
+\left\vert z^{\prime}\right\vert $

$\star$ $\left\vert zz^{\prime}\right\vert =\left\vert z\right\vert
\times\left\vert z^{\prime}\right\vert $

$\star$ $\left\vert z^{n}\right\vert =\left\vert z\right\vert ^{n}$

$\star$ $\left\vert \tfrac{z}{z^{\prime}}\right\vert =\tfrac{\left\vert
z\right\vert }{\left\vert z^{\prime}\right\vert }=\tfrac{OM}{OM^{\prime}}$

$\star$ $\left\vert re^{i\alpha}\right\vert =\left\vert r\right\vert $ donc
$\left\vert e^{i\alpha}\right\vert =1$%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion
\vspace*{-0.6cm}

\hrulefill$\vspace*{-0.4cm}$%

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$\star$ $\arg(z^{\prime}-z)=\left(  \overrightarrow{Ox};\overrightarrow
{MM^{\prime}}\right)  =\left(  \overrightarrow{Ox};\overrightarrow{M^{\prime
}M}\right)  +\pi$

$\star$ $\arg(zz^{\prime})=\arg z+\arg z^{\prime}+k2\pi$

$\star$ $\arg(z^{n})=n\arg z+k2\pi$

$\star$ $\arg\left(  \tfrac{z}{z^{\prime}}\right)  =\arg z-\arg z^{\prime
}=\left(  \overrightarrow{OM^{\prime}};\overrightarrow{OM}\right)
\quad\left[  2\pi\right]  $%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
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\end{multicols}%
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\vspace*{-0.6cm}

\hrulefill$\vspace*{-0.4cm}$%

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\begin{multicols}{2}
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$\star$ $\overrightarrow{u}$ et $\overrightarrow{v}$ orthogonaux non nuls
$\overset{z_{u}\neq0\neq z_{v}}{\Leftrightarrow}\arg(\tfrac{z_{v}}{z_{u}%
})=\tfrac{\pi}{2}+k\pi$

$\star$ $\overrightarrow{u}$ et $\overrightarrow{v}$ colin\'{e}aires non nuls
$\overset{z_{u}\neq0\neq z_{v}}{\Leftrightarrow}\arg(\tfrac{z_{v}}{z_{u}%
})=k\pi$%

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\end{multicols}%
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\vspace*{-0.6cm}

\hrulefill$\vspace*{-0.4cm}$%

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\begin{multicols}{2}
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$\star$ $%
\begin{array}
[c]{c}%
e^{i\alpha}=\cos\alpha+i\sin\alpha\\
e^{-i\alpha}=\cos\alpha-i\sin\alpha
\end{array}
$ donc $%
\begin{array}
[c]{l}%
\cos\alpha=\tfrac{1}{2}\left(  e^{i\alpha}+e^{-i\alpha}\right)
%TCIMACRO{\TeXButton{Ait�}{
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\\
\sin\alpha=\tfrac{1}{2i}\left(  e^{i\alpha}-e^{-i\alpha}\right)
\end{array}
$

$\star$ $e^{i\alpha}\cdot e^{i\alpha^{\prime}}=e^{i\alpha+\alpha^{\prime}}$

$\star$ $\sin\alpha+i\cos\alpha=e^{i\left(\tfrac{\pi}{2}-\alpha\right)  }$%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion
\vspace*{-0.45cm}

$\star\hfill$Formules de {\small Moivre}: $\left(  e^{i\alpha}\right)
^{n}=e^{in\alpha}$ donc $\left(  \cos\alpha+i\sin\alpha\right)  ^{n}=\left(
\cos n\alpha+i\sin n\alpha\right)  \quad\left(  n\in%
%TCIMACRO{\TeXButton{Z}{\mathbb{Z}}}%
%BeginExpansion
\mathbb{Z}%
%EndExpansion
\right)  $\hspace{\stretch{2}}$\vspace*{-0.25cm}$

\hrulefill$\vspace*{-0.05cm}$

$\star$ \hspace*{\fill}Translation de vecteur $\overrightarrow{u}$ d'affixe
$a:z\mapsto z^{\prime}=z+a$\hspace*{\fill}$\vspace*{-0.25cm}$%

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$\star$ {\small Rotation d'angle} $\alpha\left\{
\begin{tabular}
[c]{l|l}%
de centre $O$ & de centre $\Omega(\omega)$\\
$z^{\prime}=e^{i\alpha}z$ & $z^{\prime}-\omega=e^{i\alpha}(z-\omega)$%
\end{tabular}
\ \right.  $

$\star$ {\small Homoth\'{e}tie de rapport} $k\left\{
\begin{tabular}
[c]{l|l}%
de centre $O$ & de centre $\Omega(\omega)$\\
$z^{\prime}=kz$ & $z^{\prime}-\omega=k(z-\omega)$%
\end{tabular}
\ \right.  $%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion
\vspace*{-0.6cm}

\hrulefill

$\hspace*{\fill}az^{2}+bz+c=0\underset{a\neq0}{\overset{\Delta=b^{2}%
-4ac}{\Leftrightarrow}}\left\{
\begin{array}
[c]{ll}%
\text{Si }\Delta<0 & z=\dfrac{-b\pm i\sqrt{-\Delta}}{2a}\\
\text{Si }\Delta\geq0 & z=\dfrac{-b\pm\sqrt{\Delta}}{2a}%
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\end{array}
\right.  \overset{a\neq0}{\Leftrightarrow}\left\{
\begin{array}
[c]{l}%
z+z^{\prime}=-\dfrac{b}{a}\\
z\times z^{\prime}=\dfrac{c}{a}%
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%{\setlength{\fboxrule}{0pt}
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\end{array}
\right.  \hspace*{\fill}$

%

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\begin{boxedminipage}[t]{19.98cm}%
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\vspace*{-0.05cm}

$\star$ $p${\small -liste \`{a} }$n$ {\small choix avec remise: }$n^{p}%
\hspace*{\fill}\star$ {\small Permutations de }$n$ {\small \'{e}l\'{e}ments=}%
$n${\small -liste \`{a} }$n$ {\small choix sans remise: }$n!\hspace*{\fill}$

$\star$ {\small Arrangement de }$p$ {\small \'{e}l\'{e}ments parmi}
$n${\small =}$p${\small -liste \`{a} }$n$ {\small choix sans remise : }%
$A_{n}^{p}=\tfrac{n!}{(n-p)!}\hspace*{\fill}\star$ $\left(  a+b\right)  ^{n}=%
%TCIMACRO{\dsum \limits_{p=0}^{n}}%
%BeginExpansion
{\displaystyle\sum\limits_{p=0}^{n}}
%EndExpansion
\tbinom{n}{p}a^{n-p}b^{b}\hspace*{\fill}$\vspace*{-0.25cm}

$\star$ {\small Combinaisons de }$p$ {\small \'{e}l\'{e}ments parmi }%
$n${\small =ensemble de }$p$ {\small \'{e}l\'{e}ments parmi }$n$ {\small (ss
remise) : }$C_{n}^{p}=\tbinom{n}{p}=\tfrac{n!}{p!(n-p)!}$\vspace*{-0.1cm}

\hrulefill$\vspace*{-0.4cm}$%

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\begin{multicols}{2}%
%EndExpansion


$\star$ \'{E}quiprobabilit\'{e} : $P(A)=\tfrac{Card(A)}{Card(\Omega)}%
\hspace*{\fill}\star$ $P(\overline{A})=1-P(A)\hspace*{\fill}$

$\star$ $\vspace*{-1cm}$%
\begin{align*}
P(A\cap B)  &  =P(A)+P(B)-P(A\cup B)\\
&  =P(A)\times P(B/A)=P(B)\times P(A/B)
\end{align*}


$\star$ $A$ {\small et} $B$ {\small ind\'{e}pendants%
\begin{tabular}
[t]{l}%
$\Leftrightarrow P(A/B)=P(A)$\\
$\Leftrightarrow P(A\cap B)=P(A)\times P(B)$%
\end{tabular}
}

$\star$ $E(X)=\sum p_{i}x_{i}\hspace*{\fill}\star$ $\sigma(X)=\sqrt
{V(X)}\hspace*{\fill}$

$\star$ $V(X)=\sum p_{i}\left(  x_{i}-E(X)\right)  ^{2}=\left(  \sum
p_{i}x_{i}^{2}\right)  -E^{2}(X)$%

%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
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\end{multicols}%
%EndExpansion
\vspace*{-0.7cm}

\hrulefill$\vspace*{-0.4cm}$%

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\begin{multicols}{2}%
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$\star$ {\small Proba continue} :%

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%EndExpansion%
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%}}%
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{\setlength{\fboxrule}{0pt}
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\fbox{\rule[-1.5cm]{0pt}{3.5cm}}}
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$\hspace*{\fill}\left\{
\begin{array}
[c]{l}%
f\text{ densit\'{e}}\Leftrightarrow\left\{
\begin{array}
[c]{l}%
f\text{ continue sur }%
%TCIMACRO{\TeXButton{R}{\mathbb{R}}}%
%BeginExpansion
\mathbb{R}%
%EndExpansion
\\
f\geq0\text{ sur }%
%TCIMACRO{\TeXButton{R}{\mathbb{R}}}%
%BeginExpansion
\mathbb{R}%
%EndExpansion
\\
\int_{%
%TCIMACRO{\TeXButton{R}{\mathbb{R}}}%
%BeginExpansion
\mathbb{R}%
%EndExpansion
}f(x)dx=1
\end{array}
\right. \\
P(X=a)=0\\
P(a\leq X\leq b)=P(a<X<b)=\int_{a}^{b}f(x)dx\\
P(X\geq a)=P(X>a)=\underset{b\rightarrow+\infty}{\lim}\int_{a}^{b}f(x)dx
\end{array}
\right.  \hspace*{\fill}$%
%TCIMACRO{\TeXButton{EMinipage}{\end{minipage}}}%
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\end{minipage}%
%EndExpansion


%

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\begin{minipage}{10cm}%
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$\star$ {\small Loi uniforme sur} $\left[  a;b\right]  $:$\left\{
\begin{array}
[c]{l}%
f(x)=\tfrac{1}{b-a}\text{ sur }\left[  a;b\right] \\
P(X\in\left[  \alpha;\beta\right]  )=\tfrac{\beta-\alpha}{b-a}%
\end{array}
\right.  $

$\star$ {\tiny L exponentielle}{\small :} $\left\{  \hspace*{-0.2cm}%
\begin{array}
[c]{l}%
f(x)=\lambda e^{-\lambda x}\text{ sur }[0;+\infty\lbrack\\
P(X\geq a)=e^{-\lambda a}\\
P(a\leq X\leq b)=e^{-\lambda a}-e^{-\lambda b}\\
P(X\geq t_{0}+t_{1})=P(X\geq t_{0})\times P(X\geq t_{1})
\end{array}
\right.  $

$\star$ {\small Loi binomiale (P(1 succ\`{e}s)}$=p$):

$\hspace*{\fill}\left\{
\begin{array}
[c]{l}%
P(k\text{ {\small succ\`{e}s /} }n\text{ {\small evnts}})=\tbinom{n}{k}%
p^{k}(1-p)^{n-k}\\
E(X)=np\text{ et }V(x)=np(1-p)
\end{array}
\right.  \hspace*{\fill}$%

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\end{minipage}%
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\end{multicols}%
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\end{boxedminipage}%
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%

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%\begin{boxedminipage}[t]{19.98cm}}}%
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\begin{boxedminipage}[t]{19.98cm}%
%EndExpansion
%

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%\setlength{\columnseprule}{0pt}
%\begin{multicols}{4} }}%
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$\star$ $\sin^{2}x+\cos^{2}x=1$

$\star$ $\tan x=\tfrac{\sin x}{\cos x}$

$\star\cos2x%
\begin{array}
[t]{l}%
=2\cos^{2}x-1\\
=1-2\sin^{2}x\\
=\cos^{2}x-\sin^{2}x
\end{array}
$

$\star$ $\sin2x=2\sin x\cos x$

$\star$ $\cos^{2}x=\tfrac{1}{2}(1+\cos2x)$

$\star$ $\sin^{2}x=\tfrac{1}{2}(1-\cos2x)$

$\star$ $1+\tan^{2}x=\tfrac{1}{\cos^{2}x}$%

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\end{multicols}%
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\vspace*{-1cm}%

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$\star$ $\cos(a+b)=\cos a\cos b-\sin a\sin b$

$\star$ $\cos(a-b)=\cos a\cos b+\sin a\sin b$

$\star$ $\sin(a+b)=\sin a\cos b+\sin b\cos a$

$\star$ $\sin(a-b)=\sin a\cos b-\sin b\cos a$%

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\unboldmath
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\vfill
\begin{center}%
\scriptsize{Imprim� avec \LaTeXe}%
\end{center}
\end{document}