Mathe-Abi ab 2004
Aufgabe: Löse die Gleichung $e^{2x}+e^{x}-2=0$
Lösung:
fricas
g:=%e^(2*x)+%e^(x)-2=0
\begin{equation}
\label{eq1}{{{e}^{2 \ x}}+{{e}^{x}}- 2}= 0\end{equation}
Type: Equation(Expression(Integer))
fricas
g:=g+2
\begin{equation}
\label{eq2}{{{e}^{2 \ x}}+{{e}^{x}}}= 2\end{equation}
Type: Equation(Expression(Integer))
fricas
f:=(2*x^2+2*x-1)/(x^2-1)
\begin{equation}
\label{eq3}{{2 \ {{x}^{2}}}+{2 \ x}- 1}\over{{{x}^{2}}- 1}\end{equation}
Type: Fraction(Polynomial(Integer))
fricas
differentiate(f,x)
\begin{equation}
\label{eq4}{-{2 \ {{x}^{2}}}-{2 \ x}- 2}\over{{{x}^{4}}-{2 \ {{x}^{2}}}+ 1}\end{equation}
Type: Fraction(Polynomial(Integer))
fricas
simplify(%)
\begin{equation}
\label{eq5}{-{2 \ {{x}^{2}}}-{2 \ x}- 2}\over{{{x}^{4}}-{2 \ {{x}^{2}}}+ 1}\end{equation}
Type: Expression(Integer)
fricas
f2:=3*(x^2-4*%e^(-2*x))
\begin{equation}
\label{eq6}-{{12}\ {{e}^{-{2 \ x}}}}+{3 \ {{x}^{2}}}\end{equation}
Type: Expression(Integer)
fricas
integrate(f2,x)
\begin{equation}
\label{eq7}{6 \ {{e}^{-{2 \ x}}}}+{{x}^{3}}\end{equation}
Type: Union(Expression(Integer),...)
Comparar $ea(n)$ con ordenes como $n^k$, $2^n$, $n!$, $n^n$ donde
$ea(n)=\frac{1}{n-\log_2{2^n-1}}$
Intento:
fricas
e:=1/(n-log(2^n-1))
\begin{equation}
\label{eq8}-{1 \over{{\log \left({{{2}^{n}}- 1}\right)}- n}}\end{equation}
Type: Expression(Integer)
fricas
simplify(e)
\begin{equation}
\label{eq9}-{1 \over{{\log \left({{{2}^{n}}- 1}\right)}- n}}\end{equation}
Type: Expression(Integer)
fricas
solve(n+2-log((2^(n+1)-1)^2/(2^n-1));n)
\begin{equation*}
\label{eq10}\left[{n = 0}\right]?\end{equation*}
Type: List(Equation(Fraction(Polynomial(Integer))))
fricas
solve([nw=h/cos(a)/(h/w+tan(a)),nh=nw*h/w],[w,h])
\begin{equation*}
\label{eq11}\begin{array}{@{}l}
\displaystyle
\left[ \left[{w ={{{{{nw}^{2}}\ {\cos \left({a}\right)}\ {\tan \left({a}\right)}}+{nh \ nw \ {\cos \left({a}\right)}}}\over nh}}, \: \right.
\
\
\displaystyle
\left.{h ={{nw \ {\cos \left({a}\right)}\ {\tan \left({a}\right)}}+{nh \ {\cos \left({a}\right)}}}}\right] \right]
\end{array}
\end{equation*}
Type: List(List(Equation(Expression(Integer))))
Some or all expressions may not have rendered properly,
because Latex returned the following error:
This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6)
\write18 enabled.
%&-line parsing enabled.
entering extended mode
(./8782887868210934443-16.0px.tex
LaTeX2e <2005/12/01>
Babel <v3.8h> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, arabic, farsi, croatian, ukrainian, russian, bulgarian, czech, slov
ak, danish, dutch, finnish, basque, french, german, ngerman, ibycus, greek, mon
ogreek, ancientgreek, hungarian, italian, latin, mongolian, norsk, icelandic, i
nterlingua, turkish, coptic, romanian, welsh, serbian, slovenian, estonian, esp
eranto, uppersorbian, indonesian, polish, portuguese, spanish, catalan, galicia
n, swedish, ukenglish, pinyin, loaded.
(/usr/share/texmf-texlive/tex/latex/base/article.cls
Document Class: article 2005/09/16 v1.4f Standard LaTeX document class
(/usr/share/texmf-texlive/tex/latex/base/size12.clo))
(/usr/share/texmf-texlive/tex/latex/ucs/ucs.sty
(/usr/share/texmf-texlive/tex/latex/ucs/data/uni-global.def))
(/usr/share/texmf-texlive/tex/latex/base/inputenc.sty
(/usr/share/texmf-texlive/tex/latex/ucs/utf8x.def))
(/usr/share/texmf-texlive/tex/latex/bbm/bbm.sty)
(/usr/share/texmf-texlive/tex/latex/jknapltx/mathrsfs.sty)
(/usr/share/texmf-texlive/tex/latex/base/fontenc.sty
(/usr/share/texmf-texlive/tex/latex/base/t1enc.def))
(/usr/share/texmf-texlive/tex/latex/pstricks/pstricks.sty
(/usr/share/texmf-texlive/tex/generic/pstricks/pstricks.tex
`PSTricks' v1.15 <2006/12/22> (tvz)
(/usr/share/texmf-texlive/tex/generic/pstricks/pstricks.con))
(/usr/share/texmf/tex/latex/xcolor/xcolor.sty
(/etc/texmf/tex/latex/config/color.cfg)
(/usr/share/texmf-texlive/tex/latex/graphics/dvips.def)
(/usr/share/texmf-texlive/tex/latex/graphics/dvipsnam.def)))
(/usr/share/texmf-texlive/tex/latex/graphics/epsfig.sty
(/usr/share/texmf-texlive/tex/latex/graphics/graphicx.sty
(/usr/share/texmf-texlive/tex/latex/graphics/keyval.sty)
(/usr/share/texmf-texlive/tex/latex/graphics/graphics.sty
(/usr/share/texmf-texlive/tex/latex/graphics/trig.sty)
(/etc/texmf/tex/latex/config/graphics.cfg))))
(/usr/share/texmf-texlive/tex/latex/pst-grad/pst-grad.sty
(/usr/share/texmf-texlive/tex/generic/pst-grad/pst-grad.tex
(/usr/share/texmf-texlive/tex/latex/xkeyval/pst-xkey.tex
(/usr/share/texmf-texlive/tex/latex/xkeyval/xkeyval.sty
(/usr/share/texmf-texlive/tex/latex/xkeyval/xkeyval.tex)))
`pst-plot' v1.05, 2006/11/04 (tvz,dg,hv)))
(/usr/share/texmf-texlive/tex/latex/pstricks/pst-plot.sty
(/usr/share/texmf-texlive/tex/generic/pstricks/pst-plot.tex
v97 patch 2, 1999/12/12
(/usr/share/texmf-texlive/tex/generic/multido/multido.tex
v1.41, 2004/05/18 <tvz>)))
(/usr/share/texmf-texlive/tex/latex/geometry/geometry.sty
(/usr/share/texmf-texlive/tex/xelatex/xetexconfig/geometry.cfg)
Package geometry Warning: `lmargin' and `rmargin' result in NEGATIVE (-108.405p
t).
`width' should be shortened in length.
) (/usr/share/texmf-texlive/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `? option.
(/usr/share/texmf-texlive/tex/latex/amsmath/amstext.sty
(/usr/share/texmf-texlive/tex/latex/amsmath/amsgen.sty))
(/usr/share/texmf-texlive/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texmf-texlive/tex/latex/amsmath/amsopn.sty))
(/usr/share/texmf-texlive/tex/latex/amsfonts/amsfonts.sty)
(/usr/share/texmf-texlive/tex/latex/amsfonts/amssymb.sty)
(/usr/share/texmf-texlive/tex/latex/amscls/amsthm.sty)
(/usr/share/texmf-texlive/tex/latex/setspace/setspace.sty
Package: `setspace 6.7 <2000/12/01>
) (/usr/share/texmf-texlive/tex/generic/xypic/xy.sty
(/usr/share/texmf-texlive/tex/generic/xypic/xy.tex Bootstrap'ing: catcodes,
docmode, (/usr/share/texmf-texlive/tex/generic/xypic/xyrecat.tex)
(/usr/share/texmf-texlive/tex/generic/xypic/xyidioms.tex)
Xy-pic version 3.7 <1999/02/16>
Copyright (c) 1991-1998 by Kristoffer H. Rose <krisrose@ens-lyon.fr>
Xy-pic is free software: see the User's Guide for details.
Loading kernel: messages; fonts; allocations: state, direction,
utility macros; pictures: \xy, positions, objects, decorations;
kernel objects: directionals, circles, text; options; algorithms: directions,
edges, connections; Xy-pic loaded))
(/usr/share/texmf-texlive/tex/generic/xypic/xyall.tex
Xy-pic option: All features v.3.3
(/usr/share/texmf-texlive/tex/generic/xypic/xycurve.tex
Xy-pic option: Curve and Spline extension v.3.7 curve, circles, loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xyframe.tex
Xy-pic option: Frame and Bracket extension v.3.7 loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xycmtip.tex
Xy-pic option: Computer Modern tip extension v.3.3
(/usr/share/texmf-texlive/tex/generic/xypic/xytips.tex
Xy-pic option: More Tips extension v.3.3 loaded) loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xyline.tex
Xy-pic option: Line styles extension v.3.6 loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xyrotate.tex
Xy-pic option: Rotate and Scale extension v.3.3 loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xycolor.tex
Xy-pic option: Colour extension v.3.3 loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xymatrix.tex
Xy-pic option: Matrix feature v.3.4 loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xyarrow.tex
Xy-pic option: Arrow and Path feature v.3.5 path, \ar, loaded)
(/usr/share/texmf-texlive/tex/generic/xypic/xygraph.tex
Xy-pic option: Graph feature v.3.7 loaded) loaded)
(/usr/share/texmf-texlive/tex/latex/tools/verbatim.sty)
(/usr/share/texmf/tex/latex/graphviz/graphviz.sty
(/usr/share/texmf-texlive/tex/latex/psfrag/psfrag.sty))
(/usr/share/texmf/tex/latex/sagetex.sty
Writing sage input file 8782887868210934443-16.0px.sage
) (/usr/share/texmf-texlive/tex/latex/gnuplottex/gnuplottex.sty
(/usr/share/texmf-texlive/tex/latex/base/latexsym.sty)
(/usr/share/texmf-texlive/tex/latex/moreverb/moreverb.sty)
(/usr/share/texmf-texlive/tex/latex/base/ifthen.sty))
(./8782887868210934443-16.0px.aux)
(/usr/share/texmf-texlive/tex/latex/ucs/ucsencs.def)
(/usr/share/texmf-texlive/tex/latex/jknapltx/ursfs.fd)
(/usr/share/texmf-texlive/tex/latex/amsfonts/umsa.fd)
(/usr/share/texmf-texlive/tex/latex/amsfonts/umsb.fd)
(/usr/share/texmf-texlive/tex/latex/base/ulasy.fd) [1] [2] [3]
Package amsmath Warning: Foreign command \over;
(amsmath) \frac or \genfrac should be used instead
(amsmath) on input line 127.
[4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
Missing \right. inserted.
<inserted text>
\right .
l.152 \
Extra \right.
l.155 ...{\cos \left({a}\right)}}}}\right] \right]
[18] (./8782887868210934443-16.0px.aux) )
(see the transcript file for additional information)
Output written on 8782887868210934443-16.0px.dvi (18 pages, 5000 bytes).
Transcript written on 8782887868210934443-16.0px.log.