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%\title{DL Usuels}
%\author{Louis Dalibard}
%\date{\today}

\begin{document}
\pagebreak
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\begin{table}
\centering\setcellgapes{1pt}\makegapedcells
\makebox[\linewidth]{
  \begin{tabular}{!{\qquad}l|l!{\qquad}} \Xhline{2\arrayrulewidth}
    \hline
    A l'ordre $n$                    & Premiers termes \\ \hline
    $\cos(x) = \sum\limits_{k=0}^{n}(-1)^k\frac{x^{2k}}{(2k)!}+o_{x \rightarrow 0}(x^{2n+1}) $                         &       \begin{tabular}{!{\qquad}ccccccccc!{\qquad}} $\cos(x)$ & $=$ & $1$ & $-$ & $\frac{x^2}{2}$ & $+$ & $\frac{x^4}{24}$ & $+$ & $o_{x \rightarrow 0}(x^5)$ \\ 
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-2:2,legend pos=outer north east]
    \addplot[color=red] {cos(deg(x))}; 
    \addplot[color=blue] {1};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-2:2,legend pos=outer north east]
    \addplot[color=red] {cos(deg(x))}; 
    \addplot[color=blue] {1-x^2/2)};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-2:2,legend pos=outer north east]
    \addplot[color=red] {cos(deg(x))}; 
    \addplot[color=blue] {1-x^2/2+x^4/24};
    \end{axis}
    \end{tikzpicture}
    \end{tabular}         \\ \hline
    $\sin(x) = \sum\limits_{k=0}^{n}(-1)^k\frac{x^{2k+1}}{(2k+1)!}+o_{x \rightarrow 0}(x^{2n+2}) $                            &     \begin{tabular}{!{\qquad}ccccccccc!{\qquad}} $\sin(x)$ & $=$ & $x$ & $-$ & $\frac{x^3}{6}$ & $+$ & $\frac{x^5}{120}$ & $+$ & $o_{x \rightarrow 0}(x^6)$ \\ 
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-2:2,legend pos=outer north east]
    \addplot[color=red] {sin(deg(x))}; 
    \addplot[color=blue] {x};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-2:2,legend pos=outer north east]
    \addplot[color=red] {sin(deg(x))}; 
    \addplot[color=blue] {x-x^3/6};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-2:2,legend pos=outer north east]
    \addplot[color=red] {sin(deg(x))}; 
    \addplot[color=blue] {x-x^3/6+x^5/120};
    \end{axis}
    \end{tikzpicture}
    \end{tabular}            \\ \hline
    $e^x = \sum\limits_{k=0}^{n} \frac{x^{k}}{k!}+o_{x \rightarrow 0}(x^{n})   $                              &         \begin{tabular}{!{\qquad}ccccccccccc!{\qquad}} $e^x$ & $=$ & $1$ & $+$ & $x$ & $+$ & $\frac{x^2}{2}$ & $+$ & $\frac{x^3}{6}$ & $+$ & $o_{x \rightarrow 0}(x^3)$ \\ 
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-2:2,legend pos=outer north east]
    \addplot[color=red] {e^x}; 
    \addplot[color=blue] {1};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-2:2,legend pos=outer north east]
    \addplot[color=red] {e^x}; 
    \addplot[color=blue] {1+x)};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-2:2,legend pos=outer north east]
    \addplot[color=red] {e^x}; 
    \addplot[color=blue] {1+x+x^2/2};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-2:2,legend pos=outer north east]
    \addplot[color=red] {e^x}; 
    \addplot[color=blue] {1+x+x^2/2+x^3/6};
    \end{axis}
    \end{tikzpicture}
    \end{tabular}\\ \hline
    $ \ln(1+x) = \sum\limits_{k=0}^{n} (-1)^{k+1}\frac{x^{k}}{k}+o_{x \rightarrow 0}(x^{n})   $                         &        \begin{tabular}{!{\qquad}ccccccccc!{\qquad}} $\ln(1+x)$ & $=$ & $x$ & $-$ & $\frac{x^2}{2}$ & $+$ & $\frac{x^3}{3}$ & $+$ & $o_{x \rightarrow 0}(x^3)$ \\ 
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=0:2,legend pos=outer north east]
    \addplot[color=red] {ln(x+1)}; 
    \addplot[color=blue] {x};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=0:2,legend pos=outer north east]
    \addplot[color=red] {ln(x+1)}; 
    \addplot[color=blue] {x-x^2/2};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-1:1,legend pos=outer north east]
    \addplot[color=red] {ln(x+1)}; 
    \addplot[color=blue] {x-x^2/2+x^3/3};
    \end{axis}
    \end{tikzpicture}
    \end{tabular}         \\ \hline
    $ \frac{1}{1+x} = \sum\limits_{k=0}^{n} (-1)^k x^{k}+o_{x \rightarrow 0}(x^{n})   $ &         \begin{tabular}{!{\qquad}ccccccccccc!{\qquad}} $\frac{1}{1+x}$ & $=$ & $1$ & $-$ & $x$ & $+$ & $x^2$ & $-$ & $x^3$ & $+$ & $o_{x \rightarrow 0}(x^3)$ \\ 
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
    \addplot[color=red] {1/(1+x)}; 
    \addplot[color=blue] {1};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
    \addplot[color=red] {1/(1+x)}; 
    \addplot[color=blue] {1-x)};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
    \addplot[color=red] {1/(1+x)}; 
    \addplot[color=blue] {1-x+x^2};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
    \addplot[color=red] {1/(1+x)}; 
    \addplot[color=blue] {1-x+x^2-x^3};
    \end{axis}
    \end{tikzpicture}
    \end{tabular}        \\ \hline
    $ \frac{1}{1-x} = \sum\limits_{k=0}^{n} x^{k}+o_{x \rightarrow 0}(x^{n})   $ &       \begin{tabular}{!{\qquad}ccccccccccc!{\qquad}} $\frac{1}{1-x}$ & $=$ & $1$ & $+$ & $x$ & $+$ & $x^2$ & $+$ & $x^3$ & $+$ & $o_{x \rightarrow 0}(x^3)$ \\ 
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
    \addplot[color=red] {1/(1-x)}; 
    \addplot[color=blue] {1};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
    \addplot[color=red] {1/(1-x)}; 
    \addplot[color=blue] {1+x)};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
    \addplot[color=red] {1/(1-x)}; 
    \addplot[color=blue] {1+x+x^2};
    \end{axis}
    \end{tikzpicture}
    & & \begin{tikzpicture}[scale=0.3, transform shape]
    \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
    \addplot[color=red] {1/(1-x)}; 
    \addplot[color=blue] {1+x+x^2+x^3};
    \end{axis}
    \end{tikzpicture}
    \end{tabular}          \\ \hline
    \Xhline{2\arrayrulewidth}
  \end{tabular}
  }
\end{table}
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\end{document}
