Difference between revisions of "MR 03 Loesung"

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Line 37: Line 37:
 
<math>5\cdot \binom{5}{2}</math>
 
<math>5\cdot \binom{5}{2}</math>
  
−
<math>2\cdot \int\limits_{-5}^{5} x \, dx</math>
+
<math>\int\limits_{-5}^{5} 2\cdot x \, dx</math>
  
−
<math>4\cdot \int\limits_{-\sqrt{5}}^{\sqrt{5}} x^3 \, dx</math>
+
<math>\int\limits_{-\sqrt{5}}^{\sqrt{5}} 4\cdot x^3 \, dx</math>
  
−
<math>8\cdot \int\limits_{-\sqrt{\sqrt{5}}}^{\sqrt{\sqrt{5}}} x^7 \, dx</math>
+
<math>\int\limits_{-\sqrt{\sqrt{5}}}^{\sqrt{\sqrt{5}}} 8\cdot x^7 \, dx</math>
  
 
Fertig! Nach dem Schema der obigen 3 Formeln lassen sich <math>\infty</math> viele Formeln angeben (die Formeln unterscheiden sich alle, da in der ersten keine, in der zweiten zwei, in der dritten drei usw. Wurzeln bei den Grenzen stehen):
 
Fertig! Nach dem Schema der obigen 3 Formeln lassen sich <math>\infty</math> viele Formeln angeben (die Formeln unterscheiden sich alle, da in der ersten keine, in der zweiten zwei, in der dritten drei usw. Wurzeln bei den Grenzen stehen):
Line 53: Line 53:
 
<math>e = 2^n -1 ;</math>
 
<math>e = 2^n -1 ;</math>
  
−
<math>c\cdot \int\limits_{-a}^{a} x^e \, dx</math>
+
<math>\int\limits_{-a}^{a} c\cdot x^e \, dx</math>

Revision as of 12:20, 10 January 2014

Welche Formel ergibt 50?

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 2\cdot (3^3-2)}

Die obige Formel gilt eigentlich nicht, weil 4 Zahlen darin vorkommen.

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 2\cdot 5 \cdot 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 14+17+19}

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 {10\cdot 10}\over 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 \sqrt{4\cdot 5\cdot 125}}

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_{i\in \{1..10\} \setminus 5} i}

Die gefällt mir am Besten. Die obige Formel bedeutet: "Was ist die Summe der ersten 10 natürlichen Zahlen - ohne fünf?"

Wo wir schon bei Prosa sind; wie schnell darf man im Ortsgebiet von 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 2\cdot 3)} -axing fahren?

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 {p_{95}+1}\over 10}

Erklärung: 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 p_n} ist die n-te Primzahl.

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{\sqrt{\sqrt{17^{11}}}} + 1 \right \rfloor}

Erklärung: Die "Hacken" bedeuten: abrunden auf die nächste ganze Zahl - manchmal auch floor() genannt.

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 x^2-10x-2000 ; x \in \mathbb{R}^+ ; 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 15+\binom{7}{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 5\cdot \binom{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 \int\limits_{-5}^{5} 2\cdot x \, dx}

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\limits_{-\sqrt{5}}^{\sqrt{5}} 4\cdot x^3 \, dx}

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\limits_{-\sqrt{\sqrt{5}}}^{\sqrt{\sqrt{5}}} 8\cdot x^7 \, dx}

Fertig! Nach dem Schema der obigen 3 Formeln lassen sich 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 \infty} viele Formeln angeben (die Formeln unterscheiden sich alle, da in der ersten keine, in der zweiten zwei, in der dritten drei usw. Wurzeln bei den Grenzen stehen):

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 n \in \mathbb{N}_0 ;}

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 c = 2^{n+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 a = {\underbrace{ \sqrt{} \sqrt{} \cdots \sqrt{} }_{n\text{ Wurzeln}}} 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 e = 2^n -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 \int\limits_{-a}^{a} c\cdot x^e \, dx}

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