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\begin{document}

\begin{center}

\large \bf{

  /,    \\
 \\
HY200:   
 
=333 

\bigskip
 \noindent 2 :    :  Taylor
   -   }



\normalsize
\end{center}
\bigskip


\noindent 1:       :
\begin{center}
\begin{tabular}{|c||c|c|c|}
  % after \\: \hline or \cline{col1-col2} \cline{col3-col4} ...
  \hline
  n  & f(.3) & p(.3) &   \\ \hline \hline
  2  & 0.30769231 & -1.2500000 &96.72523090  \\ \hline
  4  & 0.30769231 & 3.81250000 &2592.075448  \\ \hline
  6  & 0.30769231 & -7.5781250 &58431.83431  \\ \hline
\end{tabular}. $\clubsuit$
\end{center}
\noindent         
         Taylor.

\noindent 2:   $f(x)=\exp(-4x^2)$ 
     matrixgenerator 
evaluatepolynomial       3,7,13,31,61
    [-3,3].    
601       [-3,3] 
    :
     3 : 0.87267038,    
     7 :0.96786931,
     13 :6.56057959,
     31 :86.64594694,
     61 :6.87406189.


 \noindent 3:        
     :
 $$
 3 \cos \left( \frac{2i+1}{n+1} \frac{\pi}{2} \right), ~~ i=0,\ldots,n
 $$
  :
     3 :0.99355898,
     7 :0.68045626,
     13 :0.20048991,
     31 :0.00047881,
     61 :0.00003506.

 \noindent ,        
       
      2 (  ). 
        .
 .

 \noindent 4:

\begin{center}
$$
\begin{array}{|c|c|}\hline

\textrm{}& \textrm{ } \\
\hline \hline

7&0.2533677\\ \hline
13&0.0115764\\ \hline
31&0.000931\\ \hline
61&0.0000524\\ \hline

\end{array}.
$$
\end{center}

\noindent         
      
. ,, spline  13   
  f(x)   0.2202801


\noindent 5.      
,         
 .    
        
   SSE=1.3911.

\noindent 6.    5 
     4      
  SSE=0.9124      8 SSE=0.6655.



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