cgi-bin/mimetex.cgi?
" align="absmiddle">
=
\,\mathbb{R}
\ \limits
_{\fs1{0}}
^{\fs1{+}}
\backslash\left{\hspace{1}
1
\hspace{1}\right}
\raisebox{5}{\begin{matrix}\fs1 \to\fs3\,\\ \\x \end{matrix}}
\ =\ \begin{pmatrix}
-7\\ \\15\\ \\-1
\end{pmatrix}
+ r\,\cdot \,\begin{pmatrix}
4\\ \\-15\\ \\-3
\end{pmatrix} mit r\raisebox{1}{\in}\mathbb R
\int
\limits_{
\fs11
\ }^{\hspace{8}
\fs12
}
\left(
-\raisebox{-2}{\frac{2}{3}}x^{\fs12}
\right)\
dx
\ =\
\left[\
-\raisebox{-2}{\frac{2}{9}}x^{\fs13}
\ \right]\
\limits_{\fs11}^{\fs12}
x\underset{\tiny >}{\to} 0
\raisebox{10}{\ }}
f(x)\ =
x\to\infty
\raisebox{10}{\ }}
f(x)\ =
\,a_{\tiny 11}\ & a_{\tiny 12}\ & a_{\tiny 13}\\
^{\,}a_{\tiny 21}\ & a_{\tiny 22}\ & a_{\tiny 23}^{\ }\\
^{\,}a_{\tiny 31}\ & a_{\tiny 32}\ & a_{\tiny 33}^{\ }
\end{pmatrix}
\ \overset{\fs1>}{\underset{\fs1<}{\longrightarrow}}\
0
\hspace{10} \compose{=}{\hspace{10}\compose{=}{\hspace{8}>}} \hspace{10}
f(x)
\ \longrightarrow\
\pm\infty
{\left(x^3 - 2x^2 - x + 2\right) : \left(x - 1\right) = x^2 - x - 2\\
\hspace{0}\underline{ x^3 - x^2}\\
\hspace{40}-x^2 - x\\
\hspace{40}\underline{-x^2 + x}\\
\hspace{80}-2x + 2\\
\hspace{80}\underline{-2x + 2}\\
\hspace{142}0}
& \end{array} %% nach & gebrochen-rationaler Anteil %%
\mathbb{L}\,=\,\left{\hspace{1}2\hspace{1}\right}
\sum \limits_{i^\,=\,0}^{_\ k_\ }
B\,\left(\,n\,,\ \frac13\,,\ i\,\right)
\sum \limits_{x\hspace{2}\raisebox{1}{\fs1 \in}X}
x \hspace{2} \cdot \hspace{2} P(X=x)
{c40|c40|c40|c40|c40|c40}
x & -2 & -1 & 0 & 1 & 2
_\ \\\hline
f(x) & 1 & 2 & 3 & 4 & 5
^\ \end{array}
{c60|c60|c90|c60|c60|c60}
& x < & -1 & < x < & 0 & < x_ \\\hline
f'(x) & - & 0 & + & n. def. & +_ \\\hline
G_f & f\ddot{a}llt & TIP\left(-1\,\left|\,\frac23\right.\right) & steigt & n. def. & steigt ^ \end{array}
x
\text{ f\ddot ur }
x\ <\ 0
_\ \\\
2x
\text{ f\ddot ur }
x\ \geq\ 0
^\ \right.
\picture(600,400){
(270,370){\text\fs{+2}Start}
(300,360){\line(-150,-100)}
(160,280){\fs{+1}0,1}
(300,360){\line(0,-100)}
(270,280){\fs{+1}0,4}
(300,360){\line(150,-100)}
(420,280){\fs{+1}0,5}
(130,233){\text\fs{+4}A}
(290,233){\text\fs{+4}B}
(455,233){\text\fs{+4}C}
(137,225){\line(-100,-100)}
(40,150){\fs{+1}0,1}
(137,225){\line(-30,-100)}
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(137,225){\line(30,-100)}
(165,150){\fs{+1}0,5}
(300,225){\line(-70,-100)}
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(300,225){\line(0,-100)}
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(300,225){\line(70,-100)}
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(470,225){\line(-30,-100)}
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(470,225){\line(30,-100)}
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(470,225){\line(100,-100)}
(540,150){\fs{+1}0,5}
(20,95){\text\fs{+4}A}
(90,95){\text\fs{+4}B}
(155,95){\text\fs{+4}C}
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(10,82){\line(580,0)}
(10,50){\text\fs{+1}0,01}
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(360,50){\text\fs{+1}0,2}
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(490,50){\text\fs{+1}0,2}
(550,50){\text\fs{+1}0,25}
\begin{array}{c|c|c|c}& A & \overline{A} & \\_{ }\\
\hline \\ B^{ }& \raisebox{-7}{\fbox[25][22]{0,1}} & 0,2 & \raisebox{-7}{\fbox[25][22]{0,3}}\\_{ }\\
\hline \overline{B}^{ }& 0,3 & 0,4 & 0,7\\_{ }\\
\hline & \raisebox{-7}{\fbox[25][22]{0,4}}^{ }& 0,6 & 1\end{array}
\begin{array}{c|ccc|c|c}& P & Q & R & Markt & Produktion \\_{ }\\
\hline P^{ }&a_{\fs111}&10&40&50&100\\_{ }\\_{ }\\
Q&0&40&a_{\fs123}&100&160\\_{ }\\_{ }\\
R&30&20&20&y_{\fs13}&200\end{array}
= \raisebox{3}{\begin{matrix}\to\\ \\y \end{matrix}} \compose{=}{=\Rightar}\\
Gau\beta-Algorithmus:\\
x\fs1_1\fs3 x\fs1_2\fs3 x\fs1_3\fs3 \\ \\
\begin{array}{ccc|cc}
0,6 & -0,2 & -0,2 & 4&\\_{ }\\
-0,9& 0,9&-0,1& 2& I\,-\,2\cdot II\\_{ }\\
0,1&-0,2& 0&-7&\\
\hline
\end{array}\\
\begin{array}{ccc|cc}
0,6 & -0,2 & -0,2 & 4&\\_{ }\\
2,4& -2& 0& 0& II\,-\,10\cdot III\\_{ }\\
0,1&-0,2& 0&-7&\\
\hline
\end{array}\\
\begin{array}{ccc|c}
\,0,6 &\,-0,2 & -0,2 & 4&&&\Rightar x_{\fs13} = 70\\_{ }\\
\,2,4&\,-2& 0& \,0&&\Rightar x_{\fs12} = 60\\_{ }\\
\,1,4& 0& 0& 70& \Rightar x_{\fs11} = 50
\end{array}\\
\compose{=}{=\Rightar} \raisebox{5}{\begin{matrix}\to\\ \\x \end{matrix}}
= \begin{pmatrix}50\\ \\60\\ \\70\end{pmatrix}