%%
%% The LaTeX Companion, 3ed
%%
%% Example 11-6-2 on page II-192 in "Operator and function names".
%%
%% Copyright (C) 2022 Frank Mittelbach
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3c
%% of this license or (at your option) any later version.
%%
%% See https://www.latex-project.org/lppl.txt for details.
%%

\documentclass{tlc3examargin}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{147.0pt}

  % Shorten the vertical size of the example ...
  \AtBeginDocument{%
    \setlength\abovedisplayskip{.7\abovedisplayskip}%
    \setlength\belowdisplayskip{.7\belowdisplayskip}%
  }

%StartShownPreambleCommands
\usepackage{amsmath} \newcommand\abs[1]{\lvert#1\rvert}
%StopShownPreambleCommands

\begin{document}
 \begin{gather*}
   \lim_{x \rightarrow 0} \frac{ \sin^2(x) }{ x^2 }=1 \\
   \varliminf_{n \rightarrow \infty}
      \abs{a_{n+1}} / \abs{a_n} = 0                   \\
   \varinjlim (m_i^\lambda \cdot M)^* \le
      \varprojlim_{A/p\rightarrow\lambda(A)}A_p \le 0
 \end{gather*}
\end{document}