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Diffstat (limited to 'Master/texmf-doc/doc/german/kopka/uebungen/kapitel5/ueb5-11.tex')
-rw-r--r-- | Master/texmf-doc/doc/german/kopka/uebungen/kapitel5/ueb5-11.tex | 17 |
1 files changed, 17 insertions, 0 deletions
diff --git a/Master/texmf-doc/doc/german/kopka/uebungen/kapitel5/ueb5-11.tex b/Master/texmf-doc/doc/german/kopka/uebungen/kapitel5/ueb5-11.tex new file mode 100644 index 00000000000..3eb6f7e0985 --- /dev/null +++ b/Master/texmf-doc/doc/german/kopka/uebungen/kapitel5/ueb5-11.tex @@ -0,0 +1,17 @@ +\documentclass{article} +\usepackage{german} +\setlength{\textwidth}{135mm} +\begin{document} +\begin{equation} +\lim_{x\to0}\frac{\sqrt{1+x} - 1}{x} = +\lim_{x\to0}\frac{(\sqrt{1+x} - 1)(\sqrt{1+x} + 1)}{x(\sqrt{1+x} + 1)} = +\lim_{x\to0}\frac{1}{\sqrt{1+x} + 1} = \frac{1}{2} +\end{equation} +\begin{equation} +\frac{\partial^2 U}{\partial x^2} + \frac{\partial^2 U}{\partial y^2} = 0\quad +\Longrightarrow\quad +U_M = \frac{1}{4\pi}\oint\limits_\Sigma\frac{1}{r}\frac{\partial U}{\partial n} +\,ds - \frac{1}{4\pi}\oint\limits_\Sigma\frac{\partial\frac{1}{r}}{\partial n} +U\,ds +\end{equation} +\end{document} |