Preambulo (para correr el latex)

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%%%-----------------------------------
%%%preambulo de los practicos de calculo II (2003)
%%%---------------------------------
\documentclass[11pt,spanish]{article}
\pagestyle{plain}
\pagestyle{empty}
%%% --- paquetes
\usepackage{amssymb}
\usepackage{babel}
\usepackage{amsmath}
\usepackage{latexsym}
\usepackage{array}
\usepackage{indentfirst}
\usepackage{amsthm}
\usepackage{calc}
\usepackage{graphics}
\usepackage{makeidx}
%%% --- Porque es tan chica la hoja ???
\addtolength{\textheight}{5cm}
\addtolength{\voffset}{-2cm}
\addtolength{\hoffset}{-1.5cm}
\addtolength{\textwidth}{2cm}
%%% --- teoremas --- demostraciones --- observaciones
\theoremstyle{plain}
\newtheorem{teorema}{Teorema}%\numberwithin{teorema}{chapter}
\newtheorem{definicion}{Definici\'on}%\numberwithin{definicion}{chapter}
\newtheorem{corolario}{Corolario}%\numberwithin{corolario}{chapter}
\newtheorem{proposicion}{Proposici\'on}%\numberwithin{proposicion}{chapter}
\newtheorem{lema}{Lema}%\numberwithin{lema}{chapter}
\newtheorem{propiedad}{Propiedad}
%%\setcounter{propiedad}{0}
\newenvironment{demostracion}
{\begin{proof}}{\renewcommand{\qed}{\hfill\qedsymbol}\end{proof}}
\theoremstyle{remark}
\newtheorem*{observacion}{Observaci\'on}
\newtheorem{ejemplo}{Ejemplo}%\numberwithin{ejemplo}{chapter}
\newtheorem*{solucion}{Soluci\'on}
\newtheorem*{aplicacion}{Aplicaci\'on}
\newtheorem*{problema}{Problema}

%% Environment ``ejercicio''

\newcounter{ejercicio}
\newenvironment{ejercicio}
{\addtocounter{ejercicio}{1}{\vskip2mm\par\noindent{\bf \theejercicio.}}}
{}

%% --- abreviaturas

\newcommand{\e}{\varepsilon}
\newcommand{\ii}{\'{\i}}

%% Nuevos comandos 

\newcommand{\tok}{\underset{k}{\longrightarrow}}        %%      tiende con k
\newcommand{\interno}[2]{\langle #1,#2\rangle}          %%      producto interno
\newcommand{\norma}[1]{\|#1\|}                          %%      norma
\newcommand{\normat}[1]
{\left|\hspace{-1pt}\left|\hspace{-1pt}\left|#1\right|\hspace{-1pt}\right|\hspace{-1pt}\right|}
%\newcommand{\normat}[1]{\left\|#1\right\|_T}            %%      norma de una transformacion lineal
\newcommand{\normai}[1]{\|#1\|_{\infty}}                %%      norma infinito
\newcommand{\normauno}[1]{\|#1\|_1}                     %%      norma uno
\newcommand{\normados}[1]{\|#1\|_2}                     %%      norma dos
\newcommand{\sucesion}[1]{#1_1,#1_2,\dots}              %%      sucesion
\newcommand{\suc}[1]{\{#1_n\}}                          %%      variante de sucesion
\newcommand{\interior}[1]{\overset{\circ}{#1}}          %%      interior de un conjunto

%%%  Operadores matematicos

\newcommand\frontera{\operatorname{\bf\delta}}  %%      frontera de un conjunto                                 
%%\newcommand{\coseno}{\operatorname{cos}}      %%      coseno
\newcommand{\sen}{\operatorname{sen}}           %%      seno
\newcommand{\tg}{\operatorname{tg}}             %%      tangente
%%\newcommand{\logaritmo}{\operatorname{log}}   %%      logaritmo
\newcommand{\Arctg}{\operatorname{Arctg}}       %%      arcotangente    
\newcommand{\sh}{\operatorname{sh}}             %%      seno hiperbolico
\newcommand{\ch}{\operatorname{ch}}             %%      coseno hiperbolico
\newcommand{\tangh}{\operatorname{th}}          %%      tangente hiperbolica
\newcommand{\Argsh}{\operatorname{Argsh}}       %%      arcoseno hiperbolico
\newcommand{\Argch}{\operatorname{Argch}}       %%      arcotangente hiperbolica
\newcommand{\Argth}{\operatorname{Argth}}       %%      acrocoseno hiperbolico
\def\det{\operatorname{\rm det}}                %%      determinante
\def\difsim{\operatorname{\triangle}}           %%      diferencia simetrica entre conjuntos
\def\mcd{\operatorname{\rm m.c.d.}}             %%      maximo comun divisor

%% Comandos renovados 
        
\renewcommand{\Im}{\operatorname{\rm Im}}       %%      parte imaginaria
\renewcommand{\Re}{\operatorname{\rm Re}}       %%      parte real
\newcommand{\derivada}[2]{{\partial #1\over\partial #2}}

%%  Negritas

\def\1{{\bf 1}}                                 %%      indicador
%% \def\A{{\bf A}}
\def\B{{\bf B}}
\def\C{{\bf C}}
\def\D{{\bf D}}
\def\I{{\bf I}}
\def\J{{\bf J}}
\def\K{{\bf K}}
\def\bfx{{\bf x}}

%% conjuntos num\'ericos

\def\R{{\mathbb R}}
\def\Z{{\mathbb Z}}
\def\N{{\mathbb N}}
\def\Q{{\mathbb Q}}
\def\rn{{\mathbb R}^n}
\def\rrm{{\mathbb R}^m}
\def\efe{f\colon X\to {\mathbb R}^m}
\def\efedos{f\colon\R^2\to\R}
\def\efeu{f\colon U\to{\mathbb R}}
\def\eFeu{F\colon U\to{\mathbb R}}
\def\geu{g\colon U\to{\mathbb R}}
%% vectores

\def\x{(x_1,\dots,x_n)}
\def\y{(y_1,\dots,y_n)}
\def\z{(z_1,\dots,z_n)}
\def\a{(a_1,\dots,a_n)}
\def\A{(A_1,\dots,A_n)}

%% Caligraficas

\def\cA{{\cal A}}
\def\cB{{\cal B}}
\def\cC{{\cal C}}
\def\cD{{\cal D}}
\def\cM{{\cal M}}

%% Serif

\def\sA{{\sf A}}

%% Complementos de conjuntos

\newlength{\mylen}
\newcommand{\myoverline}[1]{\settowidth{\mylen}{#1}
   \makebox[0pt][l]{\makebox[\mylen-0.8pt]{\hfil$\overline{\makebox[5pt]{\phantom{A}}}$\hfil}}
   {#1}}
\def\compa{\myoverline{\bf A}}
\def\compb{\myoverline{\bf B}}
\def\compc{\myoverline{\bf C}}

%% limites

%\def\ni{n\to\infty}
\def\ki{k\to\infty}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
\begin{document}
\centerline{\small Facultad de Ciencias\hfill Centro de Matem\'atica\hfill C\'alculo Diferencial e Integral II (2006)}
\vskip2mm