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Formel}\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[33,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[33,logseq____"^Flogseq____",54,536870918]],[logseq____"^15logseq____",[33,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[33,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[33,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[33,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[33,logseq____"^;logseq____",logseq____"~u652514c4-07c8-4f96-acd4-169bfe5e6240logseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&=a^2-b^2\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Flogseq____",62,536870918]],[logseq____"^15logseq____",[34,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[34,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[34,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[34,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[34,logseq____"^;logseq____",logseq____"~u652514c4-f3f0-48fe-92e7-34c4f08bb750logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&= e^x + e^y logseq____& ,f \\\\\\\\\\ne^{x+y} logseq____&= e^x * x^y logseq____& ,r \\\\\\\\\\ne^{x+y}logseq____&=e^{xy} logseq____& ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=x+y logseq____& ,x+ylogseq____>c \\\\\\\\\\ne^{ln(x+y)}logseq____&=e^x*e^ylogseq____&,f\\\\\\\\\\ne^{ln(x+y)}logseq____&=ln(e^x+y)logseq____&,x+ylogseq____>0\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Flogseq____",63,536870918]],[logseq____"^15logseq____",[35,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[35,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[35,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[35,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[35,logseq____"^;logseq____",logseq____"~u652514c4-ede3-4b01-b4c6-0a83967e3380logseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n\\\\ln a + \\\\ln b logseq____&= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&= \\\\frac1{\\\\ln a}\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Flogseq____",64,536870918]],[logseq____"^15logseq____",[36,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[36,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[36,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[36,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[36,logseq____"^;logseq____",logseq____"~u652514c4-e1ba-4d4a-a470-3a01ce3e40e1logseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Qlogseq____",logseq____"$\\\\text{Für } x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = \\\\frac{2*7}{3*5}=\\\\frac{14}{15}\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Flogseq____",67,536870918]],[logseq____"^15logseq____",[37,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[37,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[37,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[37,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[37,logseq____"^;logseq____",logseq____"~u652514c4-32e0-468d-8944-0ea8fee3689blogseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Qlogseq____",logseq____"$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=(-1)^\\\\frac22logseq____&=(-1)^1logseq____&=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=1^\\\\frac12logseq____&logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Flogseq____",44,536870918]],[logseq____"^15logseq____",[38,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[38,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[38,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[38,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[38,logseq____"^;logseq____",logseq____"~u652514c4-fa0c-4a00-a60f-dfbb43c07915logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c}\\n{0\\\\choose 0}\\n\\\\\\\\\\n{1\\\\choose 0} {1\\\\choose 1}\\n\\\\\\\\\\n{2\\\\choose 0} {2\\\\choose 1} {2\\\\choose 2}\\n\\\\\\\\\\n{3\\\\choose 0} {3\\\\choose 1} {3\\\\choose 2} {3\\\\choose 3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Flogseq____",55,536870918]],[logseq____"^15logseq____",[39,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[39,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[39,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[39,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[39,logseq____"^;logseq____",logseq____"~u652514c4-3f68-4e01-8329-4c4a37f0903blogseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Flogseq____",52,536870918]],[logseq____"^15logseq____",[40,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[40,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[40,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"~:headinglogseq____",2],536870918]],[logseq____"^15logseq____",[40,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[40,logseq____"^Hlogseq____",24,536870918]],[logseq____"^15logseq____",[40,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[40,logseq____"^;logseq____",logseq____"~u652514c4-f2a3-4160-9ae9-d2148721a408logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Flogseq____",42,536870918]],[logseq____"^15logseq____",[41,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[41,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[41,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[41,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[41,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[41,logseq____"^;logseq____",logseq____"~u652514c4-dab3-45e0-aa50-0554d6ce0ae5logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&=1logseq____&,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&= 1 logseq____&, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&=1logseq____&,r\\\\\\\\\\n1+tan^2xlogseq____&=\\\\frac1{\\\\cos^2x}logseq____&,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Flogseq____",45,536870918]],[logseq____"^15logseq____",[42,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[42,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[42,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[42,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[42,logseq____"^;logseq____",logseq____"~u652514c4-c8e3-4693-9b3b-70bf88573a75logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Qlogseq____",logseq____"logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Flogseq____",35,536870918]],[logseq____"^15logseq____",[43,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[43,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[43,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[43,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[43,logseq____"^;logseq____",logseq____"~u652514c4-c0d5-4e29-906a-bb3e51defcfclogseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____>0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a\\\\sqrt{a}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^2-\\\\sqrt{a}logseq____&,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=\\\\sqrt{a^3}logseq____&,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&=a^{\\\\frac32}logseq____&,r\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Flogseq____",58,536870918]],[logseq____"^15logseq____",[44,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[44,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[44,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[44,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[44,logseq____"^;logseq____",logseq____"~u652514c4-84be-424c-a0c5-e662a9f3cef4logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Qlogseq____",logseq____"$\\\\frac12 \\\\sqrt2, \\\\frac12, \\\\frac12\\\\sqrt3 \\\\text{ sind werte von }\\\\sin x$\\n\\\\begin{align}\\n\\\\sin 30\\\\degreelogseq____&=\\\\frac12\\\\\\\\\\n\\\\sin 45\\\\degree logseq____&= \\\\frac12\\\\sqrt2 \\\\\\\\\\n\\\\sin 60\\\\degree logseq____&= \\\\frac12 \\\\sqrt3 \\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Flogseq____",48,536870918]],[logseq____"^15logseq____",[45,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[45,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[45,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[45,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[45,logseq____"^;logseq____",logseq____"~u652514c4-5a3d-4ba7-b05d-37916613cddalogseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Flogseq____",61,536870918]],[logseq____"^15logseq____",[46,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[46,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[46,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[46,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[46,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[46,logseq____"^;logseq____",logseq____"~u652514c4-c4f8-479e-982e-208f21f66d27logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Qlogseq____",logseq____"$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&\\\\text{plus }logseq____&\\\\text{cubus }logseq____&\\\\text{acq }logseq____&6\\\\\\\\\\nxlogseq____&+logseq____&x^3logseq____&=logseq____&6\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Flogseq____",34,536870918]],[logseq____"^15logseq____",[47,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[47,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[47,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[47,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[47,logseq____"^;logseq____",logseq____"~u652514c4-1fea-457b-9f49-4c1dda6bfbe3logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Flogseq____",37,536870918]],[logseq____"^15logseq____",[48,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[48,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",28,536870918]],[logseq____"^15logseq____",[48,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[48,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[48,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[48,logseq____"^Hlogseq____",28,536870918]],[logseq____"^15logseq____",[48,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[48,logseq____"^;logseq____",logseq____"~u652514c4-612e-44ac-8a75-736473e8043clogseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Qlogseq____",logseq____"\\\\begin{array}{c} (a+b)^0logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 \\\\\\\\\\n(a+b)^1logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^2logseq____&logseq____&logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 2 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^3logseq____&logseq____&logseq____&logseq____&logseq____&1 logseq____&logseq____& 3 logseq____&logseq____& 3 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^4logseq____&logseq____&logseq____&logseq____& 1 logseq____&logseq____& 4 logseq____&logseq____& 6 logseq____&logseq____& 4 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^5logseq____&logseq____&logseq____& 1 logseq____&logseq____& 5 logseq____&logseq____& 10 logseq____&logseq____& 10 logseq____&logseq____& 5 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^6logseq____&logseq____& 1 logseq____&logseq____& 6 logseq____&logseq____& 15 logseq____&logseq____& 20 logseq____&logseq____& 15 logseq____&logseq____& 6 logseq____&logseq____& 1 \\\\\\\\\\n(a+b)^7logseq____&1 logseq____&logseq____& 7 logseq____&logseq____&21 logseq____&logseq____& 35 logseq____&logseq____& 35 logseq____&logseq____& \\\\cdots\\\\end{array}logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Flogseq____",40,536870918]],[logseq____"^15logseq____",[49,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[49,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[49,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[49,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[49,logseq____"^;logseq____",logseq____"~u652514c4-d01d-40dc-abc5-41741922a9ealogseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Qlogseq____",logseq____"$\\\\text{Die Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____>0 constraintlogseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Flogseq____",65,536870918]],[logseq____"^15logseq____",[50,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[50,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[50,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[50,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[50,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[50,logseq____"^;logseq____",logseq____"~u652514c4-daa5-42bf-ba3b-283fde719fd6logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n(2x+y)^4logseq____&=(2x)^4+4*(2x)^3y+6*(2x)^2y^2+4*2xy^3+y^4\\\\notag\\\\\\\\\\nlogseq____&=16x^4+32x^3y+24x^2y^2+8xy^3+y^4\\\\\\\\\\n(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5logseq____&=2+20x+40x^2\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Flogseq____",49,536870918]],[logseq____"^15logseq____",[51,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[51,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[51,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[51,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[51,logseq____"^;logseq____",logseq____"~u652514c4-5926-4f9c-ab69-b3d5ca9be1e0logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&=\\\\frac{2a}{2b}\\nlogseq____&=\\\\frac ab\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[52,logseq____"^Flogseq____",33,536870918]],[logseq____"^15logseq____",[52,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[52,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[52,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[52,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[52,logseq____"^;logseq____",logseq____"~u652514c4-f5d7-40a6-aa66-fd96c8823bbflogseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",51,536870918]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[53,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u652514c4-d9fc-4c4f-bcea-898e6b054781logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",41,536870918]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",27,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[54,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[54,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[54,logseq____"^Hlogseq____",27,536870918]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u652514c4-15bc-4f97-ad49-3eee5a12739alogseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",60,536870918]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^Hlogseq____",30,536870918]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u652514c4-a6c4-4e36-8a48-2f089730d368logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",43,536870918]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",25,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[56,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[56,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[56,logseq____"^Hlogseq____",25,536870918]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u652514c4-be70-4a64-85f0-9650606af42dlogseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt[n]{a^n}logseq____&=1^\\\\frac nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&=a^\\\\frac mn\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",50,536870918]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u652514c4-cb9b-4a93-a9e6-d26184f0d451logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",36,536870918]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",29,536870918]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[58,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[58,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[58,logseq____"^Hlogseq____",29,536870918]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u652514c4-1ef5-4322-8299-7a97cabf6101logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",39,536870918]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[59,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[59,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[59,logseq____"^Hlogseq____",23,536870918]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u652514c4-8f46-4aa2-ab8f-11e018ecc964logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",53,536870918]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",26,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[60,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[60,logseq____"^Hlogseq____",26,536870918]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u652514c4-245c-4915-bf2c-ac02be0c4e73logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\\\sqrt{x^4+6x^2y+9y^2}logseq____&=\\\\sqrt{(x^2+3y)^2}=x^2+3y\\\\\\\\\\n\\\\sqrt {x + \\\\sqrt{x^2-y^2}}\\\\sqrt{x-\\\\sqrt{x^2-y^2}}logseq____&=\\\\sqrt{\\\\left(x + \\\\sqrt{x^2-y^2}\\\\right)\\\\left(x-\\\\sqrt{x^2-y^2}\\\\right)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{x^2-(x^2-y^2)}\\\\notag\\\\\\\\\\nlogseq____&=\\\\sqrt{y^2}\\\\notag\\\\\\\\\\nlogseq____&=\\\\left|y\\\\right|\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",57,536870918]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u652514c4-957f-45a8-a37b-3d5b7a5a8a95logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\na^nlogseq____&=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____& a,blogseq____>0\\\\\\\\\\na^2b^2logseq____&=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&=\\\\left(\\\\frac ab\\\\right)^n\\\\\\\\\\na^na^mlogseq____&=a^{n+m}\\\\\\\\\\n\\\\frac1{a^n}logseq____&=a^{-n}\\\\\\\\\\n(a^n)^mlogseq____&=a^{nm}\\\\\\\\\\na^0logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",59,536870918]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u652514c4-8bec-4068-94e8-d0dfaf0f3b84logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",31,536870918]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[63,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[63,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[63,logseq____"^Hlogseq____",23,536870918]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",false,536870918]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u652514c4-5e32-48f6-902a-53f0db3cf1cflogseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&=\\\\lg y logseq____& ,r\\\\\\\\\\nxlogseq____&=\\\\log_y10logseq____&,f\\\\\\\\\\nxlogseq____&=\\\\log_{10}ylogseq____&,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 2 logseq____&, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, r \\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",56,536870918]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u652514c4-fe39-45c8-bf80-2455cc63292clogseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",66,536870918]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",29,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[65,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[65,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[65,logseq____"^Hlogseq____",29,536870918]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u652514c4-0a50-4d5c-b9ce-a46d8eca896dlogseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 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sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt 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Meinel, M. Mundhenk, [[\\logseq____"Mathematische Grundlagen der Informatik\\logseq____", 5. 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q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____",536870920]],[logseq____"^15logseq____",[114,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[114,logseq____"^Flogseq____",111,536870920]],[logseq____"^15logseq____",[114,logseq____"^Xlogseq____",95,536870920]],[logseq____"^15logseq____",[114,logseq____"^Vlogseq____",95,536870920]],[logseq____"^15logseq____",[114,logseq____"^Ulogseq____",80,536870920]],[logseq____"^15logseq____",[114,logseq____"^Ulogseq____",84,536870920]],[logseq____"^15logseq____",[114,logseq____"^Ulogseq____",87,536870920]],[logseq____"^15logseq____",[114,logseq____"^Ulogseq____",91,536870920]],[logseq____"^15logseq____",[114,logseq____"^Ulogseq____",95,536870920]],[logseq____"^15logseq____",[114,logseq____"^Hlogseq____",80,536870920]],[logseq____"^15logseq____",[114,logseq____"^Hlogseq____",84,536870920]],[logseq____"^15logseq____",[114,logseq____"^Hlogseq____",87,536870920]],[logseq____"^15logseq____",[114,logseq____"^Hlogseq____",91,536870920]],[logseq____"^15logseq____",[114,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[114,logseq____"^;logseq____",logseq____"~u652514c5-7156-4ff5-9ffa-ad65d97b40c6logseq____",536870920]],[logseq____"^15logseq____",[115,logseq____"^Qlogseq____",logseq____"[[Wahrheitswerteverlauf]] einer [[Aussageformel]]: Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach 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