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author | Norbert Preining <norbert@preining.info> | 2023-08-04 03:01:07 +0000 |
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committer | Norbert Preining <norbert@preining.info> | 2023-08-04 03:01:07 +0000 |
commit | 319c90e45fc96ba6f15edcf00b24e484d9d92f2b (patch) | |
tree | 7011e82643aff6842597d83574783a350142063c /info/examples/Math/09-21-1.ltx2 | |
parent | 63c1aaa794cb47fe36ebe8010257ec8ad322efbb (diff) |
CTAN sync 202308040301
Diffstat (limited to 'info/examples/Math/09-21-1.ltx2')
-rw-r--r-- | info/examples/Math/09-21-1.ltx2 | 57 |
1 files changed, 57 insertions, 0 deletions
diff --git a/info/examples/Math/09-21-1.ltx2 b/info/examples/Math/09-21-1.ltx2 new file mode 100644 index 0000000000..388f2df540 --- /dev/null +++ b/info/examples/Math/09-21-1.ltx2 @@ -0,0 +1,57 @@ +%% +%% Ein Beispiel der DANTE-Edition +%% Mathematiksatz mit LaTeX +%% 3. Auflage +%% Beispiel 09-21-1 auf Seite 203. +%% Copyright (C) 2018 Herbert Voss +%% +%% It may be distributed and/or modified under the conditions +%% of the LaTeX Project Public License, either version 1.3 +%% of this license or (at your option) any later version. +%% See http://www.latex-project.org/lppl.txt for details. +%% +%% ==== +% Show page(s) 1,2 +%% +%% +\documentclass[12pt]{screxa} +\pagestyle{empty} +\setlength\textwidth{170.40707pt} +\AtBeginDocument{\setlength\parindent{0pt}} +\usepackage[ngerman]{babel} +\usepackage[a5paper,margin=1cm]{geometry} +%StartShownPreambleCommands +\usepackage{xcolor,mdframed,amsmath} +\newcommand*\diff{\mathop{}\!\mathrm{d}} \allowdisplaybreaks +%StopShownPreambleCommands +\begin{document} +\mdfdefinestyle{theoremstyle}{linecolor=red,linewidth=2pt,frametitlerule=true,% + frametitlebackgroundcolor=gray!20,innertopmargin=\topskip} +\mdtheorem[style=theoremstyle]{definition}{Definition} +\begin{definition}[Quadratische Gleichung] \addtolength\jot{5pt} \begin{align} +f(x) &= g(x)\\ -x^{2}+6x-5 &= -\frac{1}{3}x^{2}+\frac{4}{3}x+\frac{5}{3}\\ + 0 &= \frac{2}{3}x^{2}-\frac{14}{3}x+ \frac{20}{3}\label{eq:fg}\\ + 0 &= x^{2}-7x+10\label{eq:4}\\ 0 &= (x-2)(x-5)\\ +\mathbb{L} &= \{2;\ 5\}\\[10pt] +F&=\int\limits_2^5\left(g(x)-f(x)\right)\diff x \\[10pt] +F &= \int\limits_2^5\left(\frac{2}{3}x^{2}\frac{14}{3}x+\frac{20}{3}\right)\diff x\\ + &= \left[\frac{2}{9}x^{3}-\frac{14}{6}x^{2}+\frac{20}{3}x\right]_{2}^{5}\\ + &= \underbrace{{\vphantom{\left(\frac{2}{9}\right)} \frac{2}{9}\cdot125-\frac{14}{6}\cdot25+\frac{20}{3} + \cdot5}}_{\textrm{obere Grenze}}\underbrace{\vphantom{% + \left(\frac{2}{9}\right)}-}_{-}\underbrace{\left(\frac{2}{9} + \cdot8-\frac{14}{6}\cdot4+\frac{20}{3}\cdot 2\right)}_{\textrm{untere Grenze}}\\[10pt] + &= \frac{500-1050+600}{18}-\frac{32-168+240}{18}\\ + &= \frac{50}{18}-\frac{104}{18}\\ &= -\frac{54}{18} = -3\\[10pt] +f(x) &= -x^{2}+6x-5=-\left(x^{2}-6x+5\right)\\ &= -\left(x-1\right)\left(x-5\right)\\[10pt] +f(x) &= -x^{2}+6x-5=-\left(x^{2}-6x+5\right)\\ + &= -\left(x^2-2\cdot3\cdot x+3^2-3^2+5\right)\\[-\normalbaselineskip] + & \phantom{\mathrel{{}=-{}}(}\underbrace{\phantom{x^{2}-2\cdot3\cdot + x+3^2}}_{\left(x-3\right)^2}\underbrace{\phantom{-3^2+5}}_{-4}\nonumber\\[10pt] +g(x) &= -\frac{1}{3}x^{2}+\frac{4}{3}x+\frac{5}{3}\\ &= -\frac{1}{3}\left(x^{2}-4x-5\right)\\ + &= -\frac{1}{3}\left(x+1\right)\left(x-5\right)\qquad\boxed{\mathbb{L}=\{-1;5\}}\\ +g(x) &= -\frac{1}{3}x^{2}+\frac{4}{3}x+\frac{5}{3}\\ &= -\frac{1}{3}\left(x^{2}-4x-5\right)\\ + &= -\frac{1}{3}\left(x^{2}-2\cdot2\cdot x+2^{2}-2^{2}-5\right)\\ + &= -\frac{1}{3}\left(\left(x-2\right)^{2}-9\right)\\ + &= -\frac{1}{3}\left(x-2\right)^{2}+3\qquad\boxed{SP(2;3)} +\end{align} \end{definition} +\end{document} |