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\def\du{{\mbox{\rm d$u$}}}
\def\dx{{\mbox{\rm d$x$}}}
\def\dt{{\mbox{\rm d$t$}}}
\def\dy{{\mbox{\rm d$y$}}}
\def\dz{{\mbox{\rm d$z$}}}
\def\ds{{\mbox{\rm d$s$}}}
\def\tg{{\mbox{\rm tg\,}}}
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\vspace*{-25mm}
\hspace*{30mm}
\textbf{Univerzitet u Zenici}\\
\hspace*{30mm}
\textbf{Pedago\v ski fakultet}\\
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Odsjek: Matematika i informatika\\
\hspace*{30mm}
Zenica, 14.02.2013.\\




\vspace*{15mm}
\centerline {Pismeni ispit iz predmeta \textbf{Analiza III}}







\vspace*{10mm}\textbf{1. }
Ispitati neprekidnost funkcije 
$\displaystyle{
f(x,y)=\left\{
\begin{array}{cr}
\displaystyle{\frac{x^2y^3}{2x^2+y^2}}, & (x,y)\ne (0,0) \\
0, & (x,y)= (0,0)
\end{array} \right.
}$.\\




\vspace*{5mm}\textbf{2. }
(a) Izmjeniti poredak integracije u integralu  
$\displaystyle{
\int\limits_0^1 \dy \int\limits_y^{3y}f(x,y)\,\dx
}$.\\
\vspace*{2mm}
\hspace*{6mm}
(b) Izračunati trojini integral 
$\displaystyle{I=\iiint\limits_{G} \frac{1}{(1+z)^3} \,\dx\dy\dz}$, gdje je oblast $G$ u prvom oktantu ograničena ravnima $x+y=1$, $z=x+y$, $x=0$, $y=0$, $z=0$.\\




\vspace*{5mm}\textbf{3. }
Izračunati krivoliniski integral prve vrste
$$
I=\oint\limits_C \sqrt{x^2+y^2}\,\ds
$$
gdje je $C$ krug $x^2+y^2=ax$, ($a$>0).\\





\vspace*{5mm}\textbf{4. }
Izračunati površinski integral druge vrste 
$$
I=\iint\limits_S xyz\,\dx\dy
$$
gdje je $S$ spoljna strana dijela sfere $x^2+y^2+z^2=1$, $x\ge 0$, $y\ge 0$.\\




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}













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