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%%% file:      s2.tex                                                        %%%
%%% author:    Ján Komara                                                    %%%
%%% email:     komara@fmph.uniba.sk                                          %%%
%%% copyright: public domain                                                 %%%
%%% version:   2020/10/05                                                    %%%
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\begin{document}

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\title{2. domáca úloha z predmetu 1-AIN-121 Matematika (1) ZS 2020/21}

\author{Ján Komara}

%\date{}
\date{\today}

\maketitle

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\section*{1. príklad}

Spočítajte, koľko celočíselných riešení má nasledujúci systém nerovníc:
\begin{align}
x_1 + x_2 & < 3
\label{eq}
\\
x_1 + x_2 + x_3 + x_4 + x_5 & < 18
,
\label{lt}
\end{align}
kde
$1 \leq x_1$, 
$-2 \leq x_2$,
$3 \leq x_3$,
$-4 \leq x_4 \leq 4$
a
$-5 \leq x_5$.

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\subsection*{Riešenie 1. príkladu}

Táto časť obsahuje riešenie 1. príkladu.

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\section*{2. príklad}

Určite konštantný koeficient pri člene $x^5$ v úplnom rozvoji výrazu 
\[
\left(1-2x+3x^2-4x^3\right)^{11}
.
\]

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\subsection*{Riešenie 2. príkladu}

Táto časť obsahuje riešenie 2. príkladu.

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