35 lines
916 B
Text
35 lines
916 B
Text
#import "@preview/grape-suite:1.0.0": exercise
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#import exercise: project, task, subtask
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#set text(lang: "de")
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#show: project.with(
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title: "Mathe am 31.10.2024",
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seminar: [Mathe Q2],
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show-outline: false,
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author: "Erik Grobecker",
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date: datetime(day: 31, month: 10, year: 2024) ,
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show-solutions: false
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)
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#show math.equation: set text(font: "New Computer Modern")
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= Potenzregelen
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1) $a^n dot a^m = a^(n+m)$\ #h(1em)$2^4+2^7=2^11=#calc.pow(2,11)$\
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2) $a^n + b^n = (a dot b)^n$\ #h(1em) $4^2+z^2=28^2=#calc.pow(28, 2)$\
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3) $(a^n)^m=a^(n dot m)$\ #h(1em) $(4^2)^3=4^(2 dot 3)=4^6=#calc.pow(4, 6)$
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= Ich hasse Mathe
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$b^y=x; #h(2em) y=log_b (x)$\
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$e^y=x #h(1em)<=> #h(1em) ln(x)=y$
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$e^y=e^(ln(x)) = x$ → ich hasse Mathe\
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$e^(ln(a))=a$
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$a^x=( e^(ln(a)) )^x=e^(ln(a) dot x)$ #h(3em) (siehe Regel 3)\
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Bsp. $2^10=e^(ln(2) dot 10)$
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= Hausaufgabe: S. 109 Nr. 2
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(Ableitung sollen wir weglassen)
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