- Liste à puce et texte en couleur
- \( \bbox[lightblue,5px] {\displaystyle \left.\int_{-1}^{1}x^2 \:\mathrm{d}x = \frac{x^3}{3} \right|_{1}^{-1}} \)
- \(\displaystyle \sum_{i=0,\ i\neq j}^n u_{ij}\)
- \( \displaystyle \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}\)
- \( \overbrace{1+2+\cdots+100}^{5050} \) ; \( \underbrace{a+b+\cdots+z}_{26} \)
- \( \begin{cases} a_1x+b_1y+c_1z=d_1 \\[2ex] a_2x+b_2y+c_2z=d_2 \\[2ex] a_3x+b_3y+c_3z=d_3 \end{cases} \)
- \( \bbox[orange,5px] {\overset{@}{ABC}\ \overset{x^2}{\longmapsto}\ \overset{\bullet\circ\circ\bullet}{T}} \)
- \( \underset{@}{ABC}\ \underset{x^2}{\longmapsto}\ \underset{\bullet\circ\circ\bullet}{T} \)
- \( \bbox[pink,5px] {\dfrac{1}{\sqrt{\vphantom{b} a} - \sqrt{b}}}\) versus \( \bbox[pink,5px] {\dfrac{1}{\sqrt{ a} - \sqrt{b}}} \)
- \(\begin{array}{rrrrrr|r} & x_1 & x_2 & s_1 & s_2 & s_3 & \\ \hline s_1 & 0 & 1 & 1 & 0 & 0 & 8 \\ s_2 & 1 & -1 & 0 & 1 & 0 & 4 \\ s_3 & 1 & 1 & 0 & 0 & 1 & 12 \\ \hline & -1 & -1 & 0 & 0 & 0 & 0 \end{array}\)
* \(\bbox[yellow,5px] {e^x = \lim\limits_{n \to +\infty} \left( 1+\frac{x}{n} \right)^n} \)
\[\frac{f\left(y_{n}\right)-f\left(x_{n}\right)}{y_{n}-x_{n}}-f'\left(\alpha\right)=\underbrace{\left(1-t_{n}\right)}_{\textrm{borné}}\,\underbrace{\left[T(y_n)-f'\left(\alpha\right)\right]}_{\to \, 0}+\underbrace{t_{n}}_{\textrm{borné}}\,\underbrace{\left[T(x_n)-f'\left(\alpha\right)\right]}_{\rightarrow \, 0}\]
\begin{eqnarray*}\left|\frac{f\left(y_{n}\right)-f\left(x_{n}\right)}{y_{n}-x_{n}}-f'\left(\alpha\right)\right| & = & \left|\frac{1}{y_{n}-x_{n}}\int_{x_{n}}^{y_{n}}\,\left(f'\left(t\right)-f'\left(\alpha\right)\right)\,dt\right|\\& \leqslant & \sup_{t\in\left[x_{n},y_{n}\right]}\left|f'\left(t\right)-f'\left(\alpha\right)\right|\underset{n\rightarrow\infty}{\longrightarrow}0\end{eqnarray*}
\[\bbox[#9C89FF, 5px] { \begin{array}{rcll} y & = & x^{2}+bx+c\\ & = & x^{2}+2\cdot{\displaystyle\frac{b}{2}x+c}\\ & = & \underbrace{x^{2}+2\cdot\frac{b}{2}x+\left(\frac{b}{2}\right)^{2}}-{\displaystyle \left(\frac{b}{2}\right)^{2}+c}\\ & & \qquad\left(x+{\displaystyle \frac{b}{2}}\right)^{2}\\ & = & \left(x+{\displaystyle \frac{b}{2}}\right)^{2}-\left({\displaystyle \frac{b}{2}}\right)^{2}+c & \left|+\left({\displaystyle \frac{b}{2}}\right)^{2}-c\right.\\ y+\left({\displaystyle \frac{b}{2}}\right)^{2}-c & = & \left(x+{\displaystyle \frac{b}{2}}\right)^{2} & \left|(\textrm{forme canonique})\right.\\ y-y_{S} & = & (x-x_{S})^{2}\\ S(x_{S};y_{S}) & \,\textrm{c'est-à-dire}\, & S\left(-{\displaystyle \frac{b}{2};\,\left({\displaystyle \frac{b}{2}}\right)^{2}-c}\right) \end{array} }\]
\[\bbox[lightgreen,5px] { \left( \begin{array}{c@{}c@{}c} \begin{array}{|cc|} \hline a_{11} & a_{12} \\ a_{21} & a_{22} \\ \hline \end{array} & 0 & 0 \\ 0 & \begin{array}{|ccc|} \hline b_{11} & b_{12} & b_{13}\\ b_{21} & b_{22} & b_{23}\\ b_{31} & b_{32} & b_{33}\\ \hline \end{array} & 0 \\ 0 & 0 & \begin{array}{|cc|} \hline c_{11} & c_{12} \\ c_{21} & c_{22} \\ \hline \end{array} \\ \end{array} \right) }\]
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