\documentclass{article} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{amssymb} %TCIDATA{OutputFilter=LATEX.DLL} %TCIDATA{Version=5.00.0.2570} %TCIDATA{} %TCIDATA{Created=Monday, June 25, 2001 17:45:57} %TCIDATA{LastRevised=Friday, November 16, 2007 12:59:31} %TCIDATA{} %TCIDATA{} %TCIDATA{CSTFile=On line bluem.cst} %TCIDATA{PageSetup=72,72,72,72,0} %TCIDATA{AllPages= %H=36 %F=36,\PARA{038
\QTR{small}{Matematick\U{e1} anal\U{fd}za III online - D\U{f4}kazy\dotfill \thepage }}
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\begin{document}
\author{A. U. Thor}
\title{Lab Report}
\date{The Date }
\maketitle
\begin{abstract}
A Laboratory report created with Scientific Notebook
\end{abstract}
\section{Laurentove rady}
\subsection{D\^{o}kaz vety}
\textbf{D\^{o}kaz: }a) Nech $z=a$ je odstr\'{a}nite\v{l}n\'{y} singul\'{a}%
rny bod funkcie $f,$ t.j.
\[
\lim_{z\longrightarrow a}f\left( z\right) =b,\,z\in \mathbf{C}.
\]%
Potom je $f$ v nejakom prstencovom okol\'{\i} $O_{\delta }^{\circ }\left(
a\right) $ je ohrani\v{c}en\'{a}, t.j. pre ka\v{z}d\'{e} $z\in O_{\delta
}^{\circ }\left( a\right) $ m\'{a}me $\left\vert f\left( z\right)
\right\vert \,\leq M.$ Koeficienty Laurentovho radu funkcie $f$ maj\'{u}
tvar
\[
c_{n}=\frac{1}{2\pi i}\int_{C_{r}}\frac{f\left( z\right) }{\left( z-a\right)
^{n+1}}dz,\,n=0,\,\pm 1,\,\pm 2,\dots
\]%
kde $C_{r}:\varphi _{r}:\left\langle 0,2\pi \right\rangle \longrightarrow
\mathbf{C},\,\varphi _{r}\left( t\right) =a+re^{it},\,0