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\Dauthor{�����N�l}
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\begin{document}
\chapter{�������ɋC�����悤 (����2)}
\section{``���̒l��0�ɋ߂�"�Ƃ� (�������̉��̐��x�I���E)}
������$f(x)=0$�̉��������邱�ƂƂ�,���l�I�ɂ�$f(x)\approx 0$�ƂȂ�$x$�������邱�Ƃł���.

���̂悤�ȋ�̗���l����.
\begin{equation} \label{eq1}
f(x) = x^3 - 15.70875x^2 + 61.69729x - 0.04844725
\end{equation}
�̉���,$x\approx 0.0007853982,x\approx 7.844763,x\approx 7.863201$�ł���.
���̉��̐��m����,���̌v�Z�̍ۂɐ�����ۂߌ덷�̂��߂ɗL�������ɏ�����ł�, ���̗L�������Ɠ����ɂȂ�Ƃ͌���Ȃ�.
������ۂߌ덷����̓I�Ɍ��ς���ɂ�,�O�͂ŏЉ�ꂽ���@\footnote{
�O�͕⒍�Q�ƁF�ɗ��e�L�X�gp13
}
��p���Čv�Z����΂悢.
\begin{itemize}
\item{$x\approx 0.0007853982$�̏ꍇ,\ref{eq1}�̊e���̊ۂߌ덷�̂����ł��傫���X�P�[���̊ۂߌ덷�����ƌ��ς�����̂͑�3���ł���,���̒l��$\pm 2.5*10^{-8}$�ł���.
�����,���̏ꍇ��$f(x)$�̊ۂߌ덷��$\pm 2.5*10^{-8}$�ƌ��ς�����.}
\item{$x\approx 7.844763$�̏ꍇ,\ref{eq1}�̊e���̊ۂߌ덷�͂�������قړ����X�P�[���̊ۂߌ덷��������,$f(x)$�̊ۂߌ덷��3�̍��̊ۂߌ덷�̘a�������$\pm 0.002$�ƌ��ς�����\footnote{
�e���̒l��$x^3 \approx  4.8 \times 10^2 , -15.70875 \times x^2 \approx -9.7 \times 10^2 , 61.69729 \times x \approx 4.8\times  10^2$�ƂȂ�,��������قړ����X�P�[���ƂȂ�.
����Ċe���̒l�̕��ς���������,������]�����Ď��̒l$f(x)$�̌덷�����߂��
\begin{eqnarray}
\delta f(x) &=& (3+2+1) \times \frac{20}{3} \times 10^2 \times \frac{1}{2} \times 10^{-6} \nonumber \\
&=& 20 \times 10^{-4} \nonumber \\
&=& 0.002 \nonumber
\end{eqnarray}
}
.}
\item{$x\approx 7.863201$�̏ꍇ��$x\approx 7.844763$�̏ꍇ�Ƃقړ����l�ƂȂ邽��,$f(x)$�̊ۂߌ덷��$\pm 0.002$�ƌ��ς�����.}
\end{itemize}
�ȏ���,��$f(x)$�̒l���̂��̂ɑ΂���ۂߌ덷���o�邽�߂�,���̌덷�ȏ�̐��x��$f(x)$��0�ɋ߂Â��悤�Ƃ���w�͂ɂ͈Ӗ����Ȃ�.
���_�Ƃ���,$f(x)$�̌덷�͑O�͂Ŋw�񂾌v�Z���@�ɋN��������̂Ƃ��܏�Ō���$x$�̒l�ɉ������덷�ɋN��������̂�����,�Z�@�݌v�̍ۂɂ͂��̓�̌덷���\���ɍl�����Ȃ���΂Ȃ�Ȃ��Ƃ������Ƃ��킩��.

�����,���̐��x��f(x)�̌X���ɉ����ĕς��\footnote{
��̗�͈ɗ��e�L�X�gp15�Q��
}
.
������, �ڐ��ߎ����̂����ۂ̊֐��Ȑ�����킸���ɂ���邽��, �����ł��덷����������.

������l�����,��ʂɗ��ʂ��Ă�������������\footnote{
�J��Ԃ��v�Z��p���ĕ������̉������߂悤�Ƃ���Ƃ�,�A��������$x$�̒l�̍���$\epsilon$�����ɂȂ��,����$x$�����Ƃ��č̗p������@.
}
\begin{equation}
\left| x^{(\nu )} -x^{(\nu -1)} \right| < \epsilon  
\end{equation}
���g�����v�Z�@�ɂ��Ă�,���̈ʒu�Ɍ덷�����邱�Ƃ��l�����������Ōv�Z���I���������$\epsilon$�����肵�Ȃ���΂Ȃ�Ȃ��͖̂����ł���.
������$x^{(\nu )}$��$\nu$�Ԗڂ�$x$�̂��Ƃł���.

\section{�����̐���������Ƃ��ɒ��ӂ��ׂ����� (��񗎂��E�ςݎc��)}
�����̐��̘a����鎞,���X�ɑ傫���Ȃ����Z���ɑ΂��ĉ��Z�������ΓI�ɏ������Ȃ��,�����錅���Ɍ��E�����邽�߂ɉ��Z����͂ݏo��,���邢�͂����������Z����Ȃ��Ƃ����悤�ȏ󋵂��N���蓾��.
�������񗎂�,���邢�͐ςݎc���ƌĂ�.
��̓I�ȗ�Ƃ���,���̂悤�Ȓ�ϕ����l����.
\begin{equation}
I = \int ^b _a f(x) \ dx
\end{equation}
������`���ߎ��ɂ���ĉ������Ƃ����,
\begin{equation}
I = \frac{b-a}{N} \left[ \frac{1}{2} f(a) + \sum ^{N-1} _{n=1} f \left( a + \frac{n}{N} (b-a) \right) + \frac{1}{2} f(b) \right]
\end{equation}
���v�Z���邱�ƂɂȂ�,$N$��傫�����Ă������Ƃł��{���̒l�ɋ߂Â��邱�Ƃ��ł��邪,���̑�����Z�����ו������ꏬ�����Ȃ邽��,�O�q�̐ςݎc������������\�����o�Ă��邱�ƂɂȂ�.
����������$N$�͕�������\��.


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%%%%%%%%            ���� (���x���t��)           %%%%%%%%
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%\begin{eqnarray}
% \Deqlab{1.1} % ���ȏ��ł̎��ԍ�������.
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%%%%%%%%  ���� (���ԍ���Ɨ����ď��������ꍇ)   %%%%%%%%
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% \eqno \textrm{(1.11)}
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%%%%%%%%         �Q�l���� (�{���ɏ����ꍇ)      %%%%%%%%
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%{\bfseries �Q�l����}
%\vspace{-7mm}
%\begin{description}
% \item	���Җ�, 2000:
%	���Ж�, (��, ��).
%	�o�Ŏ�, 319pp.
%\end{description}
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% \caption{
%  ���o��
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% \Dfiglab{fig0101} % ���ȏ��̐}�̔ԍ�������,
%                   % table �̐}�̏ꍇ�� tab0101
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