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 Topics FrontPage SandBox SandBox ProblemSolving <-- You are here.  Mathe-Abi ab 2004 Aufgabe: Löse die Gleichung $e^{2x}+e^{x}-2=0$ Lösung: fricasg:=%e^(2*x)+%e^(x)-2=0 \begin{equation} \label{eq1}{{{e}^{2 \ x}}+{{e}^{x}}- 2}= 0\end{equation} Type: Equation(Expression(Integer)) fricasg:=g+2 \begin{equation} \label{eq2}{{{e}^{2 \ x}}+{{e}^{x}}}= 2\end{equation} Type: Equation(Expression(Integer)) fricasf:=(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)) fricasdifferentiate(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)) fricassimplify(%) \begin{equation} \label{eq5}{-{2 \ {{x}^{2}}}-{2 \ x}- 2}\over{{{x}^{4}}-{2 \ {{x}^{2}}}+ 1}\end{equation} Type: Expression(Integer) fricasf2:=3*(x^2-4*%e^(-2*x)) \begin{equation} \label{eq6}-{{12}\ {{e}^{-{2 \ x}}}}+{3 \ {{x}^{2}}}\end{equation} Type: Expression(Integer) fricasintegrate(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: fricase:=1/(n-log(2^n-1)) \begin{equation} \label{eq8}-{1 \over{{\log \left({{{2}^{n}}- 1}\right)}- n}}\end{equation} Type: Expression(Integer) fricassimplify(e) \begin{equation} \label{eq9}-{1 \over{{\log \left({{{2}^{n}}- 1}\right)}- n}}\end{equation} Type: Expression(Integer) fricassolve(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)))) ... --Test, Fri, 04 Apr 2008 21:16:18 -0700 replyfricassolve([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 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. 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