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[Analysis] Fix Taylor Formulas

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RobinB27
2026-01-26 15:02:07 +01:00
parent 0dfbd46684
commit 181ce77fe7
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semester3/analysis-ii/cheat-sheet-rb/parts/05_diff.tex
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@@ -246,7 +246,7 @@ $$
\remark Taylor polynomials of degree $1,2$: \remark Taylor polynomials of degree $1,2$:
\begin{align*} \begin{align*}
& T_1f(y;x_0) = f(x_0) + \nabla f(x_0)\cdot y \\ & T_1f(y;x_0) = f(x_0) + \nabla f(x_0)\cdot y \\
& T_2f(y;x_0) = f(x_0) + \nabla f(x_0) \cdot y + \frac{1}{2} \Bigl( x_0^\top \cdot \textbf{H}_f(y) \cdot x_0\Bigr) & T_2f(y;x_0) = f(x_0) + \nabla f(x_0) \cdot y + \frac{1}{2} \Bigl( y^\top \cdot \textbf{H}_f(x_0) \cdot y\Bigr)
\end{align*} \end{align*}
\method Calculating $T_kf(y;x_0)$ also yields $\textbf{H}_f$ for $k \geq 2$. \method Calculating $T_kf(y;x_0)$ also yields $\textbf{H}_f$ for $k \geq 2$.