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\begin{document}
\raggedright





\renewcommand{\thesection}{}
\section{Grupa A - Pismeni ispit iz Matematike, 30.01.2014.}
\setcounter{zad}{0}



\textbf{Pravila: Ispit pisati isključivo hemiskom olovkom, prije rješenja prepisati postavku (tekst) zadatka, obratiti pažnju na matematičku kulturu i matematičku pismenost}


\begin{multicols}{2}


\begin{zad}
Rješiti sistem jednačina i diskutovati rješenja sistema u zavisnosti od parametra $\lambda$

\vspace*{-6mm}
\begin{alignat*}{9}
-x  & \,\,+\,\, & 6y &\,\,+\,\,&  (\lambda+3)z &= 21\\
-x  & \,\,+\,\, & 3y &\,\,+\,\,&  2z &= 9\\
x  & \,\,+\,\, & 3y &\,\,+\,\,&  2\lambda z &= \lambda+13 .
\end{alignat*}
\end{zad}


\vspace*{6mm}

\begin{zad}
Ispitati funkciju i nacrtati njen grafik \hspace*{20mm}$y=\displaystyle{\frac{3x^2-1}{(x^2+1)^3}}$.
\end{zad}



\begin{zad}
Odrediti integral $\displaystyle{\int\frac{6x^2-19x+9}{(x-2)(x^2-5x+6)}\dx}$.
\end{zad}






\begin{zad}
Rješiti diferencijalnu jednačinu $y'+y\,\tg x=\cos x$.
\end{zad}







\end{multicols}














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\vspace*{1mm}


\renewcommand{\thesection}{}
\section{Grupa B - Pismeni ispit iz Matematike, 30.01.2014.}
\setcounter{zad}{0}


\textbf{Pravila: Ispit pisati isključivo hemiskom olovkom, prije rješenja prepisati postavku (tekst) zadatka, obratiti pažnju na matematičku kulturu i matematičku pismenost}




\begin{multicols}{2}

\begin{zad}
Rješiti sistem jednačina i diskutovati rješenja sistema u zavisnosti od parametra $\lambda$

\vspace*{-6mm}
\begin{alignat*}{9}
-x  & \,\,+\,\, & 8y &\,\,+\,\,&  (\lambda+4)z &= 29\\
-x  & \,\,+\,\, & 4y &\,\,+\,\,&  3z &= 13\\
x  & \,\,+\,\, & 4y &\,\,+\,\,&  (2\lambda-1)z &= \lambda+16 .
\end{alignat*}
\end{zad}


\vspace*{6mm}

\begin{zad}
Ispitati funkciju i nacrtati njen grafik \hspace*{20mm}$y=\displaystyle{ \ln(2x^2-x^4) }$.
\end{zad}





\begin{zad}
Odrediti integral $\displaystyle{\int\frac{8x^2+39x+11}{(x+2)(x^2-x-6)}\dx}$.
\end{zad}



\begin{zad}
Rješiti diferencijalnu jednačinu $x^2 y^2 y'+xy^3 = y^2$.
\end{zad}





\end{multicols}




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%%\vspace*{1mm}


\renewcommand{\thesection}{}
\section{Grupa C - Pismeni ispit iz Matematike, 30.01.2014.}
\setcounter{zad}{0}



\textbf{Pravila: Ispit pisati isključivo hemiskom olovkom, prije rješenja prepisati postavku (tekst) zadatka, obratiti pažnju na matematičku kulturu i matematičku pismenost}




\begin{multicols}{2}


\begin{zad}
Rješiti sistem jednačina i diskutovati rješenja sistema u zavisnosti od parametra $\lambda$

\vspace*{-6mm}
\begin{alignat*}{9}
-x  & \,\,+\,\, & 10y &\,\,+\,\,&  (\lambda+5)z &= 37\\
-x  & \,\,+\,\, & 5y &\,\,+\,\,&  4z &= 17\\
x  & \,\,+\,\, & 5y &\,\,+\,\,&  (2\lambda-2)z &= \lambda+19 .
\end{alignat*}
\end{zad}




\vspace*{6mm}


\begin{zad}
Ispitati funkciju i nacrtati njen grafik \hspace*{20mm}$y=\displaystyle{\frac{e^x-e^{-x}}{e^x+e^{-x}}}$.
\end{zad}




\begin{zad}
Odrediti integral $\displaystyle{\int\frac{8x^2-35x+3}{(x^2+1)(x-7)}\dx}$.
\end{zad}


\begin{zad}
Rješiti diferencijalnu jednačinu $y'-y\,\sin 2x=e^{\sin^2 x}$.
\end{zad}


\end{multicols}


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%%\vspace*{1mm}


\renewcommand{\thesection}{}
\section{Grupa D - Pismeni ispit iz Matematike, 30.01.2014.}
\setcounter{zad}{0}


\textbf{Pravila: Ispit pisati isključivo hemiskom olovkom, prije rješenja prepisati postavku (tekst) zadatka, obratiti pažnju na matematičku kulturu i matematičku pismenost}




\begin{multicols}{2}


\begin{zad}
Rješiti sistem jednačina i diskutovati rješenja sistema u zavisnosti od parametra $\lambda$

\vspace*{-6mm}
\begin{alignat*}{9}
-x  & \,\,+\,\, & 8y &\,\,+\,\,&  (\lambda+4)z &= 29\\
-x  & \,\,+\,\, & 4y &\,\,+\,\,&  3z &= 13\\
x  & \,\,+\,\, & 4y &\,\,+\,\,&  (2\lambda-1)z &= \lambda+16 .
\end{alignat*}
\end{zad}




\vspace*{6mm}



\begin{zad}
Ispitati funkciju i nacrtati njen grafik \hspace*{20mm}$y=\displaystyle{ \ln(2x^2-x^4) }$.
\end{zad}





\begin{zad}
Odrediti integral $\displaystyle{\int\frac{8x^2+39x+11}{(x+2)(x^2-x-6)}\dx}$.
\end{zad}



\begin{zad}
Rješiti diferencijalnu jednačinu $x^2 y^2 y'+xy^3 = y^2$.\\
\end{zad}





\end{multicols}





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