Difference between revisions of "MR 03 Lösung rlk"
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| − | Diese Lösung ist noch nicht vollständig, ich habe noch nicht alles eingetippt, was ich mir überlegt habe und ich denke weiter nach... | + | Diese Lösung für [[MR_03]] ist noch nicht vollständig, ich habe noch nicht alles eingetippt, was ich mir überlegt habe und ich denke weiter nach... |
| − | =Die folgenden | + | =Die folgenden 17 Ausdrücke haben den Wert 50= |
| − | ==Verschiedenes ( | + | ==Verschiedenes (6)== |
<math>2\cdot 5^2</math><br> | <math>2\cdot 5^2</math><br> | ||
<math>7^2+1</math><br> | <math>7^2+1</math><br> | ||
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<math>\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left(\left(\left(1+1+1\right)!\right)!\right)!}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor | <math>\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left(\left(\left(1+1+1\right)!\right)!\right)!}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor | ||
</math> [[http://home.pipeline.com/~hbaker1/hakmem/number.html#item34| HAKMEM #34]] <br> | </math> [[http://home.pipeline.com/~hbaker1/hakmem/number.html#item34| HAKMEM #34]] <br> | ||
| + | <math>\left\lfloor\frac{\phi^{10}-\phi^{5}}{\sqrt{5}}\right\rfloor</math> mit dem Verhältnis <math>\phi=\frac{1+\sqrt{5}}{2}</math> des goldenen Schnitts<br> | ||
==Grenzwerte (3)== | ==Grenzwerte (3)== | ||
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<math>\lim_{x\to 0}100\cdot\frac{\tan(x)-\sin(x)}{x^3}</math><br> | <math>\lim_{x\to 0}100\cdot\frac{\tan(x)-\sin(x)}{x^3}</math><br> | ||
| − | ==Summen ( | + | ==Summen (5)== |
<math>\sum_{n=0}^\infty\left(\frac{49}{50}\right)^n</math><br> | <math>\sum_{n=0}^\infty\left(\frac{49}{50}\right)^n</math><br> | ||
<math>\sum_{n=-\infty}^\infty\left(\frac{7^2}{51}\right)^{|n|}</math><br> | <math>\sum_{n=-\infty}^\infty\left(\frac{7^2}{51}\right)^{|n|}</math><br> | ||
<math>3+\sum_{p\in\mathbb{P}\land p\leq 17}(p-3)</math><br> | <math>3+\sum_{p\in\mathbb{P}\land p\leq 17}(p-3)</math><br> | ||
<math>\ln(e)+\sum_{n=0}^{\infty}n\left (\frac{6}{7}\right)^{n+\exp(\mathbf{i}\pi)}</math><br> | <math>\ln(e)+\sum_{n=0}^{\infty}n\left (\frac{6}{7}\right)^{n+\exp(\mathbf{i}\pi)}</math><br> | ||
| + | <math>\sum_{n=3}^{5}n^2</math><br> | ||
| − | ==Integrale ( | + | ==Integrale (3)== |
<math>\displaystyle\int_1^{e^{50}}\frac{1}{x}\,\mathrm{d}x</math><br> | <math>\displaystyle\int_1^{e^{50}}\frac{1}{x}\,\mathrm{d}x</math><br> | ||
<math>\int_0^\pi\sin(x)\,\mathrm{d}x \cdot\int_0^\sqrt{10} y \cdot y \cdot y \,\mathrm{d}y</math><br> | <math>\int_0^\pi\sin(x)\,\mathrm{d}x \cdot\int_0^\sqrt{10} y \cdot y \cdot y \,\mathrm{d}y</math><br> | ||
| + | <math>\left\lfloor2^4 \int_{-\infty}^\infty \frac{\sin(x)}{x}\,\mathrm{d}x \right\rfloor</math><br> | ||
Latest revision as of 14:36, 15 April 2014
Diese Lösung für MR_03 ist noch nicht vollständig, ich habe noch nicht alles eingetippt, was ich mir überlegt habe und ich denke weiter nach...
Die folgenden 17 Ausdrücke haben den Wert 50
Verschiedenes (6)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2\cdot 5^2}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7^2+1}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{(\sin(\arccot(7))^2}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2(4!+1)}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left\lfloor\sqrt{\left(\left(\left(1+1+1\right)!\right)!\right)!}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor}\right\rfloor }
[HAKMEM #34]
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left\lfloor\frac{\phi^{10}-\phi^{5}}{\sqrt{5}}\right\rfloor}
mit dem Verhältnis Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi=\frac{1+\sqrt{5}}{2}}
des goldenen Schnitts
Grenzwerte (3)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\to 0}\frac{\sin(100 x)}{2 x}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\to 0}150\cdot\frac{\sinh(x)-\sin(x)}{x^3}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\to 0}100\cdot\frac{\tan(x)-\sin(x)}{x^3}}
Summen (5)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum_{n=0}^\infty\left(\frac{49}{50}\right)^n}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum_{n=-\infty}^\infty\left(\frac{7^2}{51}\right)^{|n|}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3+\sum_{p\in\mathbb{P}\land p\leq 17}(p-3)}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \ln(e)+\sum_{n=0}^{\infty}n\left (\frac{6}{7}\right)^{n+\exp(\mathbf{i}\pi)}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum_{n=3}^{5}n^2}
Integrale (3)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \displaystyle\int_1^{e^{50}}\frac{1}{x}\,\mathrm{d}x}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_0^\pi\sin(x)\,\mathrm{d}x \cdot\int_0^\sqrt{10} y \cdot y \cdot y \,\mathrm{d}y}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left\lfloor2^4 \int_{-\infty}^\infty \frac{\sin(x)}{x}\,\mathrm{d}x \right\rfloor}