62 lines
94 KiB
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62 lines
94 KiB
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1logseq____",536870918]],[logseq____"^15logseq____",[31,logseq____"^Blogseq____",1696906058902,536870918]],[logseq____"^15logseq____",[31,logseq____"^;logseq____",logseq____"~u6524bb4b-4e1d-4760-b320-5bd3bf4537a0logseq____",536870919]],[logseq____"^15logseq____",[32,logseq____"^Klogseq____",1696906058902,536870918]],[logseq____"^15logseq____",[32,logseq____"^@logseq____",false,536870918]],[logseq____"^15logseq____",[32,logseq____"^Ylogseq____",logseq____"fixmelogseq____",536870918]],[logseq____"^15logseq____",[32,logseq____"^11logseq____",logseq____"FIXMElogseq____",536870918]],[logseq____"^15logseq____",[32,logseq____"^Blogseq____",1696906058902,536870918]],[logseq____"^15logseq____",[32,logseq____"^;logseq____",logseq____"~u6524bb4a-ced2-4027-bd8e-10ad0ff847e6logseq____",536870918]],[logseq____"^15logseq____",[33,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____",[33,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[33,logseq____"^Flogseq____",58,536870918]],[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____"~u6524bb4a-0f4e-42ae-9c67-23af43550d25logseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[34,logseq____"^Flogseq____",44,536870918]],[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____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[34,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[34,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[34,logseq____"^;logseq____",logseq____"~u6524bb4a-0dfa-462d-97a2-deeac4bf4be6logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Qlogseq____",logseq____"## [[Binomialkoeffizient]]logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[35,logseq____"^Flogseq____",65,536870918]],[logseq____"^15logseq____",[35,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[35,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[35,logseq____"^Ulogseq____",26,536870918]],[logseq____"^15logseq____",[35,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[35,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"~:headinglogseq____",2],536870918]],[logseq____"^15logseq____",[35,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[35,logseq____"^Hlogseq____",26,536870918]],[logseq____"^15logseq____",[35,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[35,logseq____"^;logseq____",logseq____"~u6524bb4a-a66c-4eaa-a935-abbb7b1d297flogseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&=a^2+2ab+b^2logseq____&,\\\\text{ 1. Binomische Formel}\\\\\\\\\\n(a-b)^2logseq____&=a^2-2ab+b^2logseq____&,\\\\text{ 2. Binomische Formel}\\\\\\\\\\n(a+b)(a-b)logseq____&=a^2-b^2logseq____&,\\\\text{ 3. Binomische Formel}\\\\\\\\\\n\\\\end{align}logseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[36,logseq____"^Flogseq____",67,536870918]],[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____"~u6524bb4a-1fc0-45fd-ab65-9b2d84df60f0logseq____",536870918]],[logseq____"^15logseq____",[37,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____",[37,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[37,logseq____"^Flogseq____",63,536870918]],[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____"~u6524bb4a-c187-497e-807a-6bd222597066logseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[38,logseq____"^Flogseq____",51,536870918]],[logseq____"^15logseq____",[38,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[38,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[38,logseq____"^Ulogseq____",29,536870918]],[logseq____"^15logseq____",[38,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[38,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[38,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[38,logseq____"^Hlogseq____",29,536870918]],[logseq____"^15logseq____",[38,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[38,logseq____"^;logseq____",logseq____"~u6524bb4a-8885-4ef3-bae3-7176c29addb1logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[39,logseq____"^Flogseq____",35,536870918]],[logseq____"^15logseq____",[39,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[39,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[39,logseq____"^Ulogseq____",30,536870918]],[logseq____"^15logseq____",[39,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[39,logseq____"^Hlogseq____",30,536870918]],[logseq____"^15logseq____",[39,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[39,logseq____"^;logseq____",logseq____"~u6524bb4a-0591-40b2-86ef-81c5b03b6985logseq____",536870918]],[logseq____"^15logseq____",[40,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____",[40,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[40,logseq____"^Flogseq____",54,536870918]],[logseq____"^15logseq____",[40,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[40,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[40,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[40,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[40,logseq____"^;logseq____",logseq____"~u6524bb4a-1cf8-4588-829a-75f8aec1c78elogseq____",536870918]],[logseq____"^15logseq____",[41,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____",[41,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[41,logseq____"^Flogseq____",37,536870918]],[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____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[41,logseq____"^;logseq____",logseq____"~u6524bb4a-d67d-488d-a980-57b9b6f0b9a6logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[42,logseq____"^Flogseq____",43,536870918]],[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____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[42,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[42,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[42,logseq____"^;logseq____",logseq____"~u6524bb4a-f716-4655-a4ee-bb3be5d35499logseq____",536870918]],[logseq____"^15logseq____",[43,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____",[43,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[43,logseq____"^Flogseq____",49,536870918]],[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____"~u6524bb4a-3030-4aa5-858a-970de86b0006logseq____",536870918]],[logseq____"^15logseq____",[44,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____",[44,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[44,logseq____"^Flogseq____",53,536870918]],[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____"~u6524bb4a-b920-4e72-9e5f-9749e39bb11blogseq____",536870918]],[logseq____"^15logseq____",[45,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____",[45,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[45,logseq____"^Flogseq____",55,536870918]],[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____"~u6524bb4a-0df5-4bce-9a71-c1bcd444b6calogseq____",536870918]],[logseq____"^15logseq____",[46,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____",[46,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[46,logseq____"^Flogseq____",40,536870918]],[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____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[46,logseq____"^;logseq____",logseq____"~u6524bb4a-8855-4e76-8784-2093126ebfablogseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Qlogseq____",logseq____"logseq____<h1 style=logseq____'color: #ff0000logseq____'logseq____>MISSING IMAGElogseq____</h1logseq____>logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[47,logseq____"^Flogseq____",64,536870918]],[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____"~u6524bb4a-a4e9-4f10-8af7-0723a1683539logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[48,logseq____"^Flogseq____",33,536870918]],[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____"~u6524bb4a-733a-48b8-94e7-5019b581e058logseq____",536870918]],[logseq____"^15logseq____",[49,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____",[49,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[49,logseq____"^Flogseq____",48,536870918]],[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____"~u6524bb4a-f281-4428-b3be-8dc1c4dc1ac9logseq____",536870918]],[logseq____"^15logseq____",[50,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____",[50,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[50,logseq____"^Flogseq____",59,536870918]],[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____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[50,logseq____"^;logseq____",logseq____"~u6524bb4a-6765-44f0-a78b-2120ed7db4c5logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Qlogseq____",logseq____"cosa -logseq____> beliebige Variable\\ncubus -logseq____> hoch 3logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[51,logseq____"^Flogseq____",46,536870918]],[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____"~u6524bb4a-b8b6-4d4e-9527-1847ab3889f5logseq____",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____",36,536870918]],[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____"~u6524bb4a-57d7-4368-a4ce-2118b4a9f605logseq____",536870918]],[logseq____"^15logseq____",[53,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____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",56,536870918]],[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____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u6524bb4a-dddd-44a5-932d-06efe9b9bae8logseq____",536870918]],[logseq____"^15logseq____",[54,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____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",66,536870918]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u6524bb4a-1be4-49c5-bd04-6d7a7fadb0e8logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",52,536870918]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",24,536870918]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[55,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870918]],[logseq____"^15logseq____",[55,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[55,logseq____"^Hlogseq____",24,536870918]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u6524bb4a-8edd-4925-aa4f-c2e6b7c340f3logseq____",536870918]],[logseq____"^15logseq____",[56,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____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",38,536870918]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[56,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u6524bb4a-ce60-4d67-9c6e-e78953d2f4a7logseq____",536870918]],[logseq____"^15logseq____",[57,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____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",45,536870918]],[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____"~u6524bb4a-0930-498d-99ba-929589ad3200logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"# Was ist Größer?logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",62,536870918]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",31,536870918]],[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____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u6524bb4a-a2d4-42f1-8c8f-cb2b03222575logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Wurzeln]]logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",41,536870918]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",29,536870918]],[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____",29,536870918]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u6524bb4a-3c32-4297-9d4c-584aef43dcb3logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[60,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870918]],[logseq____"^15logseq____",[60,logseq____"^Jlogseq____",[],536870918]],[logseq____"^15logseq____",[60,logseq____"^Hlogseq____",23,536870918]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",false,536870918]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u6524bb4a-a207-42bd-8fa5-c2e0d4e3a807logseq____",536870918]],[logseq____"^15logseq____",[61,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____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",39,536870918]],[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____"~u6524bb4a-11e6-44e3-844e-0dbb83e17ce0logseq____",536870918]],[logseq____"^15logseq____",[62,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____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",50,536870918]],[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____"~u6524bb4a-465f-4858-8a98-980bbea482cclogseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",68,536870918]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",25,536870918]],[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____",25,536870918]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u6524bb4a-5f7d-43b0-bb33-681d5f5e8138logseq____",536870918]],[logseq____"^15logseq____",[64,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____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",60,536870918]],[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____"~u6524bb4a-f3c5-4056-b2dc-50c32f53c3f9logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",57,536870918]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",32,536870918]],[logseq____"^15logseq____",[65,logseq____"^Hlogseq____",32,536870918]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870918]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u6524bb4a-3a6f-413b-a4c5-a89f1e122d25logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Qlogseq____",logseq____"# [[Potenzen]]logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870918]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",61,536870918]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",31,536870918]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",31,536870918]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",23,536870918]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",31,536870918]],[logseq____"^15logseq____",[66,logseq____"^?logseq____",[logseq____"^ 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