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\begin{document}
\raggedright


\renewcommand{\thesection}{}
\section{Grupa A, 19.09.2013., ispit pisati hemiskom olovkom}
\setcounter{zad}{0}


\begin{zad}
Riješiti matričnu jednačinu 
$\displaystyle{
X\cdot(-2)=\left[\begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix}\right]+X
\left[\begin{matrix}
1 & 2 & 3\\
-4 & -5 & -6 \\
\end{matrix}\right]
\left[\begin{matrix}
-1 & -8 \\
7 & 1 \\
-2 & -4 \\
\end{matrix}\right].
}$
\end{zad}


\begin{zad}
Bez upotrebe H'Lopitalovog pravila izračunati limes
$\displaystyle{
\lim_{x \to -2} \frac{-5x^2-30x-40}{-3x^2+6x+24}
}$.
\end{zad}


\begin{zad}
Odrediti definiciono područje, znak te ekstreme funkcije
$\displaystyle{
y=\ln\frac{x}{x^2-1}
}$.
\end{zad}


\begin{zad}
Izračunati integral 
$\displaystyle{
\int x\ln(x-1)\dx
}$.
\end{zad}


\begin{zad}
Odrediti stacionarne tačke funkcije 
$\displaystyle{
z=\frac{1}{2}x^2-xy+xy^2-\frac{1}{2}x^2y
}$.
\end{zad}

\begin{zad}
Riješiti diferencijalnu jednačinu 
$\displaystyle{
y=xy'+\frac{1}{2}y'^2
}$.
\end{zad}


















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\section{Grupa B, 19.09.2013., ispit pisati hemiskom olovkom}
\setcounter{zad}{0}


\begin{zad}
Riješiti matričnu jednačinu 
$\displaystyle{
X \left[\begin{matrix}
-1 & -2 & -3\\
4 & 5 & 6 \\
\end{matrix}\right]
\left[\begin{matrix}
1 & 8 \\
-7 & -1 \\
2 & 4 \\
\end{matrix}\right]=X\cdot(-1)+
\left[\begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix}\right].
}$
\end{zad}


\begin{zad}
Bez upotrebe H'Lopitalovog pravila izračunati limes
$\displaystyle{
\lim_{x \to -4} \frac{-4x^2-12x+16}{-2x^2-10x-8}
}$.
\end{zad}


\begin{zad}
Odrediti definiciono područje, znak te ekstreme funkcije
$\displaystyle{
y=\ln\frac{x-1}{x^2+1}
}$.
\end{zad}


\begin{zad}
Izračunati integral 
$\displaystyle{
\int \ln(1+x^2)\dx
}$.
\end{zad}


\begin{zad}
Odrediti stacionarne tačke funkcije 
$\displaystyle{
z=9x^2-\frac{9}{2}x^2y+6xy^2-12xy
}$.
\end{zad}

\begin{zad}
Riješiti diferencijalnu jednačinu 
$\displaystyle{
y=-y'^2+xy'
}$.
\end{zad}







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\section{Grupa C, 19.09.2013., ispit pisati hemiskom olovkom}
\setcounter{zad}{0}


\begin{zad}
Riješiti matričnu jednačinu 
$\displaystyle{
\left[\begin{matrix}
-1 & 2 & -3\\
4 & -5 & 6 \\
\end{matrix}\right]
\left[\begin{matrix}
1 & -8 \\
7 & -1 \\
2 & -4 \\
\end{matrix}\right]X=
\left[\begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix}\right]-2X.
}$
\end{zad}


\begin{zad}
Bez upotrebe H'Lopitalovog pravila izračunati limes
$\displaystyle{
\lim_{x \to -6} \frac{3x^2+12x-36}{2x^2+10x-12}
}$.
\end{zad}


\begin{zad}
Odrediti definiciono područje, znak te ekstreme funkcije
$\displaystyle{
y=\ln\frac{x^2-1}{x+1}
}$.
\end{zad}


\begin{zad}
Izračunati integral 
$\displaystyle{
\int \ln(x^2-1)\dx
}$.
\end{zad}


\begin{zad}
Odrediti stacionarne tačke funkcije 
$\displaystyle{
z=x^2y-\frac{1}{2}xy^2-xy+\frac{1}{2}y^2
}$.
\end{zad}

\begin{zad}
Riješiti diferencijalnu jednačinu 
$\displaystyle{
1+y'^2=(y-y'x)^2
}$.
\end{zad}










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\section{Grupa D, 19.09.2013., ispit pisati hemiskom olovkom}
\setcounter{zad}{0}


\begin{zad}
Riješiti matričnu jednačinu 
$\displaystyle{
3X=\left[\begin{matrix}
1 & 2 & 3\\
4 & 5 & 6 \\
\end{matrix}\right]
\left[\begin{matrix}
-1 & 8 \\
-7 & 1 \\
2 & 4 \\
\end{matrix}\right]X+
\left[\begin{matrix}
1 & 0 \\
0 & 1 \\
\end{matrix}\right].
}$
\end{zad}


\begin{zad}
Bez upotrebe H'Lopitalovog pravila izračunati limes
$\displaystyle{
\lim_{x \to -8} \frac{5x^2+35x-40}{-2x^2-6x+80}
}$.
\end{zad}


\begin{zad}
Odrediti definiciono područje, znak te ekstreme funkcije
$\displaystyle{
y=\ln\frac{x+1}{x-1}
}$.
\end{zad}


\begin{zad}
Izračunati integral 
$\displaystyle{
\int (x+1)\ln x\dx
}$.
\end{zad}


\begin{zad}
Odrediti stacionarne tačke funkcije 
$\displaystyle{
z=6x^2y-\frac{9}{2}xy^2-12xy+9y^2
}$.
\end{zad}

\begin{zad}
Riješiti diferencijalnu jednačinu 
$\displaystyle{
y-\sqrt{4+y'^2}=y'x
}$.
\end{zad}













\end{document}