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    {\Large Izpit iz numeri"cnih metod.}\\
        	17. junij 2003\\[3cm]
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\begin{enumerate}
\item Poi"s"cite stevilo $m$ tako, da bo iteracaija 
$$	
    x=g(x),\quad g(x)=x-m\,\frac{f(x)}{f'(x)}
$$
kjer je 
$$
    f(x)=x^2-2\,x+1
$$
kar najhitreje konvergirala h korenu ena"cbe $f(x)=0$. 
\item Izra"cunajte integral  
$$
    \int_{0}^1\frac{e^x}{\sqrt{x}}\,dx
$$ 
\item Izra"cunaj neskon"cno normo matrike $A$, $\|A\|_\infty$.
$$
 A = \left[ \matrix{1 & 2 & -1\cr
                    0 & 3 & -1\cr
                    5 & -1 & 1} \right]
$$
\end{enumerate}
\newpage
\begin{verbatim}
------------------------------------------------------
1. 	m=2 
 	f=x^2+2*x+1
 	g=x-m*f/diff(f)
	-1/2*m*x+x-1/2*m
 	diff(g)
	1-1/2*m 
2. 
	2.9253034918143632176080971737140 
	int(taylor(exp(x),0,4)/sqrt(x),x,0,1)
	2.9142857142857142857142857142857
	int(taylor(exp(x),0,4)/sqrt(x),x)
	=2*x^(1/2)+2/3*x^(3/2)+1/5*x^(5/2)+1/21*x^(7/2)
3.
	norm(A,inf)
	7
-------------------------------------------------------
\end{verbatim}
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