mirror of
https://github.com/MartinThoma/LaTeX-examples.git
synced 2025-04-26 06:48:04 +02:00
20 lines
562 B
TeX
20 lines
562 B
TeX
\section*{Aufgabe 3}
|
|
\[f' (x,y) = \begin{pmatrix}
|
|
3 & \cos y\\
|
|
3 x^2 & e^y
|
|
\end{pmatrix}\]
|
|
|
|
Und jetzt die Berechnung
|
|
|
|
\[f'(x, y) \cdot (x_0, y_0) = f(x,y)\]
|
|
|
|
LR-Zerlegung für $f'(x, y)$:
|
|
|
|
\begin{align}
|
|
L &= \begin{pmatrix}1 &0 \\ \frac{1}{9} & 1\end{pmatrix}\\
|
|
R &= \begin{pmatrix}3 & \cos y \\ 0 & e^y - x^2 \cos y\end{pmatrix}\\
|
|
P &= I_2\\
|
|
-f ( \frac{-1}{3}, 0) &= \begin{pmatrix} 2\\ -\frac{1}{27}\end{pmatrix}\\
|
|
c &= \begin{pmatrix} 2\\ \frac{7}{27} \end{pmatrix}\\
|
|
(x_1, y_1) &= \begin{pmatrix} \frac{5}{3}\\ \frac{7}{27}\end{pmatrix}
|
|
\end{align}
|