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\section{Pismeni ispit iz Analize III, 10.06.2013.\\ ispit pisati isključivo hemiskom olovkom}
\setcounter{zad}{0}



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[e]{{
\begin{zad}
Funkciju definisanu grafikom razviti u Furijer-ov red. Dobijeni rezultat iskoristiti za sumiranje reda\\
$\displaystyle{\frac{1}{1\cdot 3}-\frac{3}{5\cdot 7}+...+}$
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$\displaystyle{+\frac{n\sin\frac{n\pi}{2}}{(2n-1)(2n+1)}}+...$.
\end{zad}}}
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\begin{zad}
(25\%) ($a$) Odrediti ekstreme funkcije $f(x,y)=x^2-xy+y^2-2x-2y$.

\hspace*{1mm}
(75\%) ($b$) Izračunati integral
$$
\iiint\limits_{\Omega}\sqrt{x^2+y^2+z^2}\dx\dy\dz
$$
gdje je $\Omega=\{(x,y,z)\in\R^3\,|\,x^2+y^2+z^2\le z,\, x^2+y^2\le z^2\}$.
\end{zad}

\begin{zad}
Izračunati krivoliniski integral druge vrste 
$\displaystyle{
I=\oint\limits_C (y-z)\dx+(z-x)\dy+(x-y)\dz
}$
gdje je $C$ krug $x^2+y^2+z^2=a^2$ ($a>0$), $y=x\tg\alpha$, ($0<\alpha<\frac{\pi}{2}$) uzet u smjeru suprotnom kretanju kazaljnke na satu ako se posmatra sa pozitivnog dijela $x$-ose.
\end{zad}


\begin{zad}
Izračunati površinski integral 
$\displaystyle{
I=\iint\limits_S\frac{\dS}{(1+z)^2}
}$
ako je $S$ sfera $x^2+y^2+z^2=1$.
\end{zad}




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\centerline{
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}


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