Difference between revisions of "MR 03 Lösung rlk"
(Die ersten 10 Formeln.) |
(Jetzt sind es 13.) |
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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 ist noch nicht vollständig, ich habe noch nicht alles eingetippt, was ich mir überlegt habe und ich denke weiter nach... | ||
| − | =Die folgenden | + | =Die folgenden 13 Ausdrücke haben den Wert 50= |
| − | ==Verschiedenes ( | + | ==Verschiedenes (4)== |
| + | <math>2\cdot 5^2</math><br> | ||
| + | <math>7^2+1</math><br> | ||
| + | <math>\frac{1}{(\sin(\arccot(7))^2}</math><br> | ||
<math>2(4!+1)</math><br> | <math>2(4!+1)</math><br> | ||
| + | |||
==Grenzwerte (3)== | ==Grenzwerte (3)== | ||
<math>\lim_{x\to 0}\frac{\sin(100 x)}{2 x}</math><br> | <math>\lim_{x\to 0}\frac{\sin(100 x)}{2 x}</math><br> | ||
| Line 9: | Line 13: | ||
<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 (4)== |
| + | <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>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> | ||
| + | ==Integrale (2)== | ||
| + | <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> | ||
Revision as of 14:56, 26 January 2014
Diese Lösung ist noch nicht vollständig, ich habe noch nicht alles eingetippt, was ich mir überlegt habe und ich denke weiter nach...
Die folgenden 13 Ausdrücke haben den Wert 50
Verschiedenes (4)
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)}
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 (4)
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)}}
Integrale (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 \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}