1
   \documentclass[12pt,a4paper,final]{article}
\usepackage[left=1.5cm,right=1.5cm,top=1cm,bottom=2cm]{geometry}
\usepackage{amsmath,amssymb,amsfonts}
\usepackage{graphicx}
\usepackage{tabularx}
\usepackage{array}
\usepackage{polyglossia}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setmainlanguage[numerals = maghrib, calendar = gregorian]{arabic}
\setotherlanguage{english}
\setmainfont[Ligatures=TeX]{Amiri}
\newfontfamily\arabicfont[Script=Arabic,Scale=1.15]{Amiri}
\begin{document}
\large
\setnonlatin
\vspace{0.25cm}
\begin{center}
\renewcommand{\arraystretch}{1.8}
\begin{tabular}{|c|c|}
\hline
النهاية 
& 
التعريف
\\
\hline
$\lim\limits_{x\to x_0} f(x)=\ell$ 
&
$\forall\varepsilon>0, \exists \delta_{\varepsilon}>0, \forall x\in D_f:\,  |x-x_0|\leq \delta\Rightarrow |f(x)-\ell|\leq \varepsilon$
\\
\hline
$\lim\limits_{x\to x_0} f(x)=+\infty$
&
$\forall A>0, \exists \delta_{A}>0, \forall x\in D_f:\,  |x-x_0|\leq \delta\Rightarrow f(x)\geq A$
\\
\hline
\end{tabular}
\end{center}
\end{document}

I want the in the center, and each definition under the other

Thank you

2

I'm not sure that, from a pedagogical point of view, such a table is useful.

Anyway, you can improve it by removing almost all the rules and avoiding center alignment. In order to align all “lim” symbols, I used the trick of measuring the widest subscript and typeset all subscripts in a box with the same width.

\documentclass[12pt,a4paper,final]{article}
\usepackage[left=1.5cm,right=1.5cm,top=1cm,bottom=2cm]{geometry}
\usepackage{amsmath,amssymb,mathtools}
\usepackage{array,booktabs}
\usepackage{fontspec}
\usepackage{polyglossia}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setmainlanguage[numerals = maghrib, calendar = gregorian]{arabic}
\setotherlanguage{english}
\setmainfont[Ligatures=TeX]{Amiri}
\newfontfamily\arabicfont[Script=Arabic,Scale=1.15]{Amiri}

\begin{document}

\begin{center}
\large
\setnonlatin
\settowidth{\dimen0}{$\scriptstyle x\to-\infty$}
\newcommand{\fl}[1]{\mathmakebox[\dimen0]{#1}}
\begin{tabular}{ll}
\toprule\multicolumn{1}{c}{النهاية} & \multicolumn{1}{c}{التعريف} \\
\midrule
\addlinespace
$\lim\limits_{\fl{x\to x_0}} f(x)=\ell$ 
&
$\forall\varepsilon>0, \exists \delta_{\varepsilon}>0, \forall x\in D_f:\,  |x-x_0|\leq \delta\Rightarrow |f(x)-\ell|\leq \varepsilon$
\\\addlinespace
$\lim\limits_{\fl{x\to x_0}} f(x)=+\infty$
&
$\forall A>0, \exists \delta_{A}>0, \forall x\in D_f:\,  |x-x_0|\leq \delta\Rightarrow f(x)\geq A$
\\\addlinespace
$\lim\limits_{\fl{x\to x_0}} f(x)=-\infty$
&
$\forall A<0, \exists \delta_{A}>0, \forall x\in D_f:\,  |x-x_0|\leq \delta\Rightarrow f(x)\leq A$
\\\addlinespace
$\lim\limits_{\fl{x\to +\infty}} f(x)=\ell$
&
$\forall \varepsilon>0, \exists B>0, \forall x\in D_f:\,  x\geq B\Rightarrow |f(x)-f(x_0)|\leq \varepsilon$
\\\addlinespace
$\lim\limits_{\fl{x\to +\infty}} f(x)=+\infty$
&
$\forall A>0, \exists B>0, \forall x\in D_f:\,  x\geq B\Rightarrow f(x)\geq A$
\\\addlinespace
$\lim\limits_{\fl{x\to +\infty}} f(x)=-\infty$
&
$\forall A<0, \exists B>0, \forall x\in D_f:\,  x\leq B\Rightarrow f(x)\leq A$
\\\addlinespace
$\lim\limits_{\fl{x\to -\infty}} f(x)=\ell$
&
$\forall \varepsilon>0, \exists B<0, \forall x\in D_f:\,  x\leq B\Rightarrow |f(x)-f(x_0)|\leq \varepsilon$
\\\addlinespace
$\lim\limits_{\fl{x\to -\infty}} f(x)=+\infty$
&
$\forall A>0, \exists B<0, \forall x\in D_f:\,  x\leq B\Rightarrow f(x)\geq A$
\\\addlinespace
$\lim\limits_{\fl{x\to -\infty}} f(x)=-\infty$
&
$\forall A<0, \exists B<0, \forall x\in D_f:\,  x\leq B\Rightarrow f(x)\leq A$
\\\addlinespace
\bottomrule
\end{tabular}
\end{center}
\end{document}

enter image description here

If you really want a less readable “caged” table, you can use a phantom in order to vertically center the text in a larger space.

\documentclass[12pt,a4paper,final]{article}
\usepackage[left=1.5cm,right=1.5cm,top=1cm,bottom=2cm]{geometry}
\usepackage{amsmath,amssymb,mathtools}
\usepackage{array,booktabs}
\usepackage{fontspec}
\usepackage{polyglossia}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setmainlanguage[numerals = maghrib, calendar = gregorian]{arabic}
\setotherlanguage{english}
\setmainfont[Ligatures=TeX]{Amiri}
\newfontfamily\arabicfont[Script=Arabic,Scale=1.15]{Amiri}

\begin{document}

\begin{center}
\large
\setnonlatin
\settowidth{\dimen0}{$\scriptstyle x\to-\infty$}
\newcommand{\fl}[1]{\mathmakebox[\dimen0]{#1}}
\begin{tabular}{| >{$\displaystyle}l<{$} | >{$}l<{\vphantom{\Bigg|}$} |}
\hline
\multicolumn{1}{|c|}{النهاية} & \multicolumn{1}{c|}{التعريف} \\
\hline
\lim\limits_{\fl{x\to x_0}} f(x)=\ell 
&
\forall\varepsilon>0, \exists \delta_{\varepsilon}>0, \forall x\in D_f:\,  |x-x_0|\leq \delta\Rightarrow |f(x)-\ell|\leq \varepsilon
\\\hline
\lim\limits_{\fl{x\to x_0}} f(x)=+\infty
&
\forall A>0, \exists \delta_{A}>0, \forall x\in D_f:\,  |x-x_0|\leq \delta\Rightarrow f(x)\geq A
\\\hline
\lim\limits_{\fl{x\to x_0}} f(x)=-\infty
&
\forall A<0, \exists \delta_{A}>0, \forall x\in D_f:\,  |x-x_0|\leq \delta\Rightarrow f(x)\leq A
\\\hline
\lim\limits_{\fl{x\to +\infty}} f(x)=\ell
&
\forall \varepsilon>0, \exists B>0, \forall x\in D_f:\,  x\geq B\Rightarrow |f(x)-f(x_0)|\leq \varepsilon
\\\hline
\lim\limits_{\fl{x\to +\infty}} f(x)=+\infty
&
\forall A>0, \exists B>0, \forall x\in D_f:\,  x\geq B\Rightarrow f(x)\geq A
\\\hline
\lim\limits_{\fl{x\to +\infty}} f(x)=-\infty
&
\forall A<0, \exists B>0, \forall x\in D_f:\,  x\leq B\Rightarrow f(x)\leq A
\\\hline
\lim\limits_{\fl{x\to -\infty}} f(x)=\ell
&
\forall \varepsilon>0, \exists B<0, \forall x\in D_f:\,  x\leq B\Rightarrow |f(x)-f(x_0)|\leq \varepsilon
\\\hline
\lim\limits_{\fl{x\to -\infty}} f(x)=+\infty
&
\forall A>0, \exists B<0, \forall x\in D_f:\,  x\leq B\Rightarrow f(x)\geq A
\\\hline
\lim\limits_{\fl{x\to -\infty}} f(x)=-\infty
&
\forall A<0, \exists B<0, \forall x\in D_f:\,  x\leq B\Rightarrow f(x)\leq A
\\\hline
\end{tabular}
\end{center}
\end{document}

enter image description here

  • I can't delete the center rule and the other rules, is there an other way ? – Poline Sandra Jan 20 at 15:16
  • 1
    @PolineSandra There's little hope to improve a caged table. Anyway, I added a try at it. – egreg Jan 20 at 15:26
  • it gives me a lot of errors @egreg – Poline Sandra Jan 20 at 15:40
  • @PolineSandra Not to me. Check the loaded packages: I added mathtools. – egreg Jan 20 at 15:41

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