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last edited 11 years ago by test1 |
Edit detail for SandBox ProblemSolving revision 3 of 3
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Editor: test1
Time: 2013/04/30 13:18:50 GMT+0 |
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changed: -g:=%e**(2*x)+%e**(x)-2=0 g:=%e^(2*x)+%e^(x)-2=0
Mathe-Abi ab 2004Aufgabe: 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,\begin{equation} \label{eq4}{-{2 \ {{x}^{2}}}-{2 \ x}- 2}\over{{{x}^{4}}-{2 \ {{x}^{2}}}+ 1}\end{equation}x) 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,\begin{equation} \label{eq7}{6 \ {{e}^{-{2 \ x}}}}+{{x}^{3}}\end{equation}x) 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)),\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*}nh=nw*h/w], [w, h]) Type: List(List(Equation(Expression(Integer))))
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