diff --git a/cheat-sheets/analysis/Analysis_Wichtige_Formeln.tex b/cheat-sheets/analysis/Analysis_Wichtige_Formeln.tex index 2d903ec..3d91bf8 100644 --- a/cheat-sheets/analysis/Analysis_Wichtige_Formeln.tex +++ b/cheat-sheets/analysis/Analysis_Wichtige_Formeln.tex @@ -18,7 +18,7 @@ /Keywords (Analysis I; Formeln) } -\everymath={\displaystyle} +%\everymath={\displaystyle} \begin{document} @@ -65,14 +65,11 @@ e^x &= \sum_{n = 0}^{\infty} \frac {x^n}{n!} \\ (x + y)^n &= \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k \end{align*} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Ableitungen} - -\begin{align*} - (\log x)' &= \frac{1}{x} -\end{align*} - +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{table}[ht] -\begin{minipage}[b]{0.5\linewidth}\centering +\begin{minipage}[b]{0.3\linewidth}\centering \begin{align*} (\sin x)' &= \cos x \\ (\cos x)' &= -\sin x \\ @@ -82,8 +79,8 @@ e^x &= \sum_{n = 0}^{\infty} \frac {x^n}{n!} \\ \end{align*} \end{minipage} -\hspace{0.5cm} -\begin{minipage}[b]{0.5\linewidth} +\hspace{0.1cm} +\begin{minipage}[b]{0.3\linewidth} \centering \begin{align*} @@ -94,14 +91,23 @@ e^x &= \sum_{n = 0}^{\infty} \frac {x^n}{n!} \\ % (\arccosh x)' &= \frac {1}{\sqrt{(1-x^2) \cdot (1+x^2)}} \\ % (\arctanh x)' &= \frac {1}{1 - x^2} \end{align*} - +\end{minipage} +\hspace{0.1cm} +\begin{minipage}[b]{0.3\linewidth} +\centering +\begin{align*} + (\log x)' &= \frac{1}{x} \\ +\end{align*} \end{minipage} \end{table} -\section{Potenzreihen} -Zuerst den Potenzradius r berechnen: -\( - r = \frac {1}{\lim \text{sup} \sqrt[n]{|a_n|}} -\) +\section{Werte} +\begin{table}[h] + \centering + \begin{tabular}{llll} + \(\arctan(0) = 0\) & \(\sin(0) = 0\) & \(\cos(0) = 1\) \\ + \(\arctan(1) = \frac{\pi}{4}\) & \(\sin(\frac{\pi}{2}) = 1\) & \(\cos(\frac{\pi}{2}) = 0\)\\ + \end{tabular} +\end{table} \end{document} diff --git a/tikz/vector-triangle-inequality/vector-triangle-inequality.tex b/tikz/vector-triangle-inequality/vector-triangle-inequality.tex index 4b0fb2d..151169e 100644 --- a/tikz/vector-triangle-inequality/vector-triangle-inequality.tex +++ b/tikz/vector-triangle-inequality/vector-triangle-inequality.tex @@ -17,8 +17,8 @@ % Draw the triangle \path[fill=blue!10, fill=blue!5] (A) -- (B) -- (C) -- (A); - \draw[ultra thick, xvectorcolor, arrows={-latex}] (A) -- (C) node[sloped,midway,above=-0.1cm] {$\mathsf{x}$}; - \draw[ultra thick, blue!80, arrows={-latex}] (C) -- (B) node[sloped,midway,above=-0.1cm] {$\mathsf{y}$}; - \draw[ultra thick, red!80, arrows={-latex},line cap=round] (A) -- (B) node[sloped,midway,right=-0.3cm,above=-0.1cm] {$\mathsf{z = x+y}$}; + \draw[ultra thick, xvectorcolor, arrows={-latex}] (A) -- (C) node[sloped,midway,above=-0.1cm] {$x$}; + \draw[ultra thick, blue!80, arrows={-latex}] (C) -- (B) node[sloped,midway,above=-0.1cm] {$y$}; + \draw[ultra thick, red!80, arrows={-latex},line cap=round] (A) -- (B) node[sloped,midway,right=-0.3cm,above=-0.1cm] {$x+y$}; \end{tikzpicture} \end{document}