79 lines
1.6 KiB
Typst
79 lines
1.6 KiB
Typst
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#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: [Letzte Stunde vor der Klausur],
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seminar: [Mathe Q2],
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show-outline: true,
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author: "Erik Grobecker",
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date: datetime(day: 18, month: 11, 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 Math")
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= Wiederholung Kettenregel
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Volle Ausschreibung der Kettenregel:
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$
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f(x)&=e^(2x+4)\
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&= #text(green, $ underbrace(e, "äußere Funtkion") $)^( #text(red, $ overbrace(2x+4, "innere Funtkion")$))\
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&=g(t(x))\
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#text(green, $g(u)&=e^u #h(1em) "(äußere Funkion)"$)\
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#text(red, $t(x)&=2x+4 #h(1em) "(innere Funktion)"$)\
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f'(x)&=g'(t(x)) dot t'(x)\
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g'(u)&=e\
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g'(t(x))&=e^(2x+4)\
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t'(x)&=2\
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f'(x)&=e^(2x+4) dot 2
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$
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asd:
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$
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f(x)&=-e^(-x)\
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g(u)&=-e^u\
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t(x)&=-x\
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\
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g'(u)&= -e\
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g'(t(x))&=-e^(-x)\
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t'(x)&= -1\
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\
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f'(x)&=-e^(-x) dot (-1)\
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&=e^(-x)
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$
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$g$=äußere\
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$t$=innere
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#pagebreak()
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= Sachaufgaben
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(S. 113 Nr. 1a)
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// siehe "MA_2024-11-11.typ"
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#table(
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columns: (auto, auto, auto, auto, auto, auto, auto),
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[$n$], [0], [1], [2], [3], [4], [5],
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[$B(n)$], [28], [35], [44], [58], [70], [90],
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[$B(n)/B(n-1)$],
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[],
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[$#calc.abs(35/28)$],
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[$#calc.round(calc.abs(44/35), digits: 2)$],
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[$#calc.round(calc.abs(58/44), digits: 2)$],
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[$#calc.round(calc.abs(70/58), digits: 2)$],
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[$#calc.round(calc.abs(90/70), digits: 2)$],
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)
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Sollte hier immer ungefähr der selbe Wert herauskommen, kann es sich um einen Exponenten handelt.
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= Klausur
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Schwerpunkt: Funtkionsuntersuchungen mit $e$-Funktion
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