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adding latex

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Debucquoy
2023-09-21 08:24:22 +02:00
parent 4fd7542f03
commit 4de4dcf2c2
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\relax
\providecommand\babel@aux[2]{}
\@nameuse{bbl@beforestart}
\babel@aux{nil}{}
\gdef \@abspage@last{1}

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\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[french]{babel}
\usepackage{amsmath, amsfonts, amssymb, amsthm}
\begin{document}
Il faut bien distinguer les trois epsilons, \`a savoir,
\[
\varepsilon > 0, \epsilon \text{ et } x \in A.
\]
\end{document}

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\relax
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\@nameuse{bbl@beforestart}
\babel@aux{nil}{}
\gdef \@abspage@last{1}

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This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Arch Linux) (preloaded format=pdflatex 2023.9.19) 19 SEP 2023 14:33
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See the babel package documentation for explanation.
Type H <return> for immediate help.
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l.4373 \ProcessOptions*
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\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[french]{babel}
\usepackage{amsmath, amsfonts, amssymb, amsthm}
\begin{document}
Une fonction $f : [0,1] \to \mathbb{R}$ est continue si
\[
\forall x \in [0,1], \forall \varepsilon > 0, \exists \delta > 0, \forall y \in [0,1] : \vert y - x \vert < \delta \implies \vert f(y) - f(x) \vert < \varepsilon
\]
\end{document}

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Type H <return> for immediate help.
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l.4373 \ProcessOptions*
?
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\documentclass{article}
\usepackage[utf8]{inputenc}
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\begin{document}
Imaginons que l'on veuille regarder la somme $\sum^{-1}_{k=-n} \frac{1}{|k|}(x_k -x_{k-1}) + x_0 + \sum^n_{k=1} \frac{1}{k}(x_x - x_{k-1})$. Ce n'est pas aussi lisible que l'expression suivante:
\[
\sum^{-1}_{k=-n} \frac{1}{|k|}(x_k -x_{k-1}) + x_0 + \sum^n_{k=1} \frac{1}{k}(x_x - x_{k-1})
\]
par contre il serait fou d'\'ecrire: Soit \[ f \] une fonction
\end{document}

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\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[french]{babel}
\usepackage{amsmath, amsfonts, amssymb, amsthm}
\begin{document}
Soit $f$ une fonction continue sur $[0,1], p > 1$ et $\epsilon > 0$. Alors il existe un polynome $g$ tel que
\[
||f-g||_p = (\int_0^1 |f(x) - g(x)|^p dx)^{1/p}
\]
Par exemple, on peut l'appliquer aux fonctions $f(x) = sin(x), ln(x), e^x, ...$
\end{document}

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\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[french]{babel}
\usepackage{amsmath, amsfonts, amssymb, amsthm}
\begin{document}
\[
P(X \in [\frac{k}{2^n},\frac{k+1}{2^n}]) \leq \frac{1}{n}\text{ Var}(X)
\]
\[
P\Big(X \in [\frac{k}{2^n},\frac{k+1}{2^n}]\Big) \leq \frac{\text{ Var}(X)}{n}
\]
\[
x_n \to 0 \text{ quand } n \to \infty
\]
\[
q(x,y) = \langle x,y \rangle
\]
\[
[\widehat{f}(x)]^b_a = \widehat{f}(b) - \widehat{f}(a)
\]
\[
x \in ]0,1]
\]
\[
\pi = 3,141559
\]
\end{document}

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\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[french]{babel}
\usepackage{amsmath, amsfonts, amssymb, amsthm}
\begin{document}
Tous les math\'ematiciens ne sont pas Fran\c{c}ais. Par exemple, F\'elix Mart\'inez et N\'u\~nez Vald\'es sont Espagnols, Otto H\"older est Allemand, Aleksander Pe\l czy\'nski est Polonais, Ana Sliep\v{c}evi\'c est Croate, etc
\end{document}

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?
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\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[french]{babel}
\usepackage{amsmath, amsfonts, amssymb, amsthm}
\begin{document}
Il faut changer le style avec \textbf{mod\'eration}. Si on met \textif{trop de texte} en \'evidence,
cela pourrait porter \'a confusion ou \^etre tout simplement \textbf{moche}. La commade \verb!\emph! est particuli\`erement utile.
\begin{center}
Dans un text normal, elle \'ecrit un \emph{mot} en italique
\textif{Dans un texte en italique, elle \'ecrit \emph{un mot} en style droit.}
\end{center}
\end{document}

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\documentclass{article}
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\begin{document}
\noindent C'est \'a gauche \hfill c'est \'a droite \\
C'est \'a gauche\hfill c'est au centre \hfill c'est \'a droite
\end{document}