diff --git a/tex/analysis_2/3_calculus_nvars.tex b/tex/analysis_2/3_calculus_nvars.tex index 1ca2ea8..0ae2f6c 100644 --- a/tex/analysis_2/3_calculus_nvars.tex +++ b/tex/analysis_2/3_calculus_nvars.tex @@ -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