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{\large\centerline{\textbf{Priprema za kolokvijum,}}\vspace{0.15 cm}
\centerline{\textbf{30.12.2014. godine}}\vspace{0.25 cm}

1. \textbf{$\mathbf{[20}$ bodova $]$}  Odrediti  parametar $a$ tako da funkcija \begin{equation}  \label{jedan} y=\frac{3-2a}{1+a}x+\frac{4-a}{a-3}\end{equation} bude opadaju\' ca i da se\v ce pozitivan deo $y$-ose.
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2. \textbf{$\mathbf{[20}$ bodova $]$} Slu\v cajna veli\v cina $X$ ima $N(0;1)$ raspodelu, a slu\v cajna veli\v cina $Y$ data je sa
$$Y=\left\{
\begin{array}{rl}
1, & 0,5\leq x<1,25\\
2, & \mbox{van}
\end{array}
\right. .$$
\emph{Na\' ci o\v cekivanje i disperziju slu\v cajne veli\v cine} $Y$. \vskip5pt



3. \textbf{$[\mathbf{20}$ bodova $]$} Grafi\v ckom metodom  re\v siti sistem:\begin{eqnarray}3x&+&2y=26;\\ 6x&-&3y=3  \label{dva}.\end{eqnarray}   \vskip5pt

4. \textbf{$[\mathbf{20}$ bodova $]$} \begin{flushright} \textit{Pomo\' cu jedna\v cina} (\ref{jedan}) i (\ref{dva}) \textit{napraviti novi sistem jedna\v cina.}\end{flushright}
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5. \textbf{$[\mathbf{20}$ bodova $]$}Pomo\' cu formule  pravougaonika odrediti pribli\v znu vrednost integrala $$\int\limits_{2}^5 \frac{lnx}{\big(x-1\big)^{3/2}}dx.$$
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6. \textbf{[Bonus zadatak]} \verb"Ispitati da li je" \begin{equation}2 = \sqrt{ x + \sqrt{ x + \sqrt{ x + \cdots }}}.\end{equation}

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