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\section{Prvi parcijalni iz Analize III, 26.11.2013.\\ ispit pisati isključivo hemijskom olovkom, prije rješenja prepisati tekst zadatka}
\setcounter{zad}{0}







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\begin{zad}
Dio grafika funkcije $y=f(x)$ prikazan je na slici lijevo. Datu funkciju pretvoriti u Furijer-ov red samo po cos-inusima. Dobijeni rezultat iskoristiti za sumiranje reda $\displaystyle{\sum_{n=1}^\infty \frac{1}{n}}$.
\end{zad}}}
{fig:text}




\begin{zad}
($40\%$)($a$) Ako postoji, izračunati limes: $\displaystyle{
\lim_{(x,y)\to(0,0)}\frac{\sin(x)\cdot\sin(y)}{x^2+y^2}.
}$


($60\%$)($b$) Izračunati $\displaystyle{
\lim_{(x,y)\to(0,0)}\frac{y (2^x-1)}{\sin(xy)}
}$.
\end{zad}






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




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\begin{zad}
($30\%$) Dati dvostruki integral $\displaystyle{\int_0^2\dx\int_0^x f(x,y)\dy}$ iz pravougaonih transformisati na polarne koordinate.\\ \vspace*{0mm}\\ \hspace*{7mm}
($70\%$) Izračunati $\displaystyle{
I=4\iint\limits_D xy(x^2+y^2)e^{{(xy)}^{2}}\dx\dy}$ gdje je $D=\{(x,y):1\le x^2-y^2\le 4, 1\le xy\le 3, x>0, y>0\}$ (za izgled datih krivih vidi sliku desno).
\end{zad}}}
{fig:text}




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\centerline{
Zadaci su skinuti sa stranice 
\underline{pf.unze.ba\slash nabokov}.}
\centerline{
Za uočene greške pisati na {\it infoarrt@gmail.com}
}


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