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20 lines
554 B
TeX
20 lines
554 B
TeX
\section*{Aufgabe 3}
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\[f' (x,y) = \begin{pmatrix}
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3 & \cos y\\
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3 x^2 & e^y
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\end{pmatrix}\]
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Und jetzt die Berechnung
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\[f'(x, y) \cdot (x_0, y_0) = f(x,y)\]
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LR-Zerlegung für $f'(x, y)$:
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\begin{align}
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L &= \begin{pmatrix}1 &0 \\ x^2 & 1\end{pmatrix}\\
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R &= \begin{pmatrix}3 & \cos y \\ 0 & e^y - x^2 \cos y\end{pmatrix}\\
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P &= I_2\\
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-f ( \frac{-1}{3}, 0) &= \begin{pmatrix} 2\\ -\frac{1}{27}\end{pmatrix}\\
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c &= \begin{pmatrix} 2\\ \frac{7}{27} \end{pmatrix}\\
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(x_1, y_1) &= \begin{pmatrix} \frac{5}{3}\\ \frac{7}{27}\end{pmatrix}
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\end{align}
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