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fix taylor
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LuckeeDev committed Jan 7, 2024
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2 changes: 1 addition & 1 deletion tex/analysis_2/3_calculus_nvars.tex
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Expand Up @@ -196,7 +196,7 @@ \section{Derivate di ordine superiore}
Sia $A \subseteq \R^n$ un aperto. Se $f \in \C{k}(A, \R)$, allora vale la seguente
\begin{align*}
f(\vb{x_0}+ \vb{h})= f(\vb{x_0})&+\sum_{j=1}^{n}\frac{\partial f}{\partial x_j}(\vb{x_0})h_j + \frac{1}{2}\sum_{i,j=1}^{n}\frac{\partial^2 f}{\partial x_i \partial x_j}(\vb{x_0})h_ih_j+\cdots+\\
&+\frac{1}{k!}\sum_{i_1,\dots,i_k=1}^n\frac{\partial^k}{\partial x_{i_1}\cdots\partial x_{i_k}}(\vb{x_0})h_{i_1}\cdots h_{i_k} +\\
&+\frac{1}{k!}\sum_{i_1,\dots,i_k=1}^n\frac{\partial^k f}{\partial x_{i_1}\cdots\partial x_{i_k}}(\vb{x_0})h_{i_1}\cdots h_{i_k} +\\
&+o (\norm{\vb{h}}^k) \with \norm{\vb{h}} \to 0
\end{align*}
\qed
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