From 741c44aae02c7e05c11dd320c0800e1556daeb36 Mon Sep 17 00:00:00 2001 From: Erik Grobecker Date: Tue, 10 Dec 2024 10:06:44 +0100 Subject: [PATCH] Mathe am 09.12.2024 --- INDEX.md | 1 + schule/mathe/MA_2024-12-09.typ | 129 ++++++++++++++++++++++++++++ schule/mathe/pdfs/MA_2024-12-09.pdf | Bin 0 -> 28699 bytes 3 files changed, 130 insertions(+) create mode 100644 schule/mathe/MA_2024-12-09.typ create mode 100644 schule/mathe/pdfs/MA_2024-12-09.pdf diff --git a/INDEX.md b/INDEX.md index 7389653..df4b849 100644 --- a/INDEX.md +++ b/INDEX.md @@ -95,6 +95,7 @@ | | 31.10.2024 | [hier](./schule/mathe/pdfs/MA_2024-10-31.pdf) | | **$e$-Funktionen**: Letzte Stunde vor der Klausur | 21.11.2024 | [hier](./schule/mathe/pdfs/MA_2024-11-21.pdf) | | Stunde nach der Klausur | 05.12.2024 | [hier](./schule/mathe/pdfs/MA_2024-12-05.pdf) | +| Verknüpfung von Funktionen | 09.12.2024 | [hier](./schule/mathe/pdfs/MA_2024-12-09.pdf) | Zusammenfassungen: diff --git a/schule/mathe/MA_2024-12-09.typ b/schule/mathe/MA_2024-12-09.typ new file mode 100644 index 0000000..9f3d501 --- /dev/null +++ b/schule/mathe/MA_2024-12-09.typ @@ -0,0 +1,129 @@ +#import "@preview/grape-suite:1.0.0": exercise +#import exercise: project, task, subtask + +#set text(lang: "de") + +#show: project.with( + title: [Wie werden Funktionen verknüpft], + seminar: [Mathe Q2], + // show-outline: true, + author: "Erik Grobecker", + date: datetime(day: 9, month: 12, year: 2024), +) + += Ganzrationale Funktionen + +Wiederholung: +$ + f(x) &= underbrace(3x^2, "Pf") #h(0.5em) underbrace(+2x, "Pf") #h(0.5em) underbrace(+1, "Pf") +$ + +Ganzrationale Funktionen bestehen aus einer Summe oder Differenz von Potenzfunktionen(Pf).\ +Man sie ab mittels der Potenz- und Summenregel. + += Kettenregel + +Beispiel: +$ + f(x)&= e^(2x+1)\ + g(u)&=e^u\ + t(x)&=2x+1\ + g(t(x)) &= f(x)\ + #line(stroke: (dash: "dashed"))\ + f'(x)&=g'(t(x)) dot t'(x)\ + f'(x) &= e^(2x+1) dot 2 + +$ + +== Aufgaben +S. 139 Nr. a) - f) + +$ + a) #h(0.25em) & f'(x) =& 4(x+2)^3\ + b) #h(0.25em) & f'(x) =& 24(8x+2)^2\ + c) #h(0.25em) & f'(x) =& 15(1/2 -5x)^2\ + d) #h(0.25em) & f'(x) =& x(x^2-5)\ + e) #h(0.25em) & f'(x) =& 2e^(2x)\ + f) #h(0.25em) & f'(x) =& -4e^(-4x) + +$ + +Nr. 3 a) & b) + +$ + a)\ + f(x) &= 2e^x\ + f'(x) &= 2e^x\ + \ + g(x) &= 0.5(1-3x)^4\ + g'(x) &= -6(1-3x)^3 + \ + b)\ + f(x) &= (5-2x)^4\ + f'(x) &= -8(5-2x)^3\ + \ + g(x)&=4 dot e^(2-x)\ + g'(x)&=-4 dot e^(2-x) +$ + += Produktregel + +$ + f(x) &= x^2 dot e^(3x)\ + f'(x) &= 2x dot 3e^(3x) #h(1em) ???\ + \ + f(x) &= u dot v\ + f'(x)&= u'(x) dot v(x) + u(x) dot v'(x)\ + u(x)&= x^2\ + u'(x)&=2x\ + v(x)&= e^(3x)\ + v'(x)&=e^(3x) dot 3\ + &=3e^(3x)\ + f'(x)&= 2x dot 3e^(3x) + x^2 dot 3e^(3x) +$ + +$ + g(x)&=e^(3x)\ + t(u)&=e^u\ + j(x)&=3x +$ + +#pagebreak() + +== Übung +S. 136 Nr. 1a) - d) + +$ + a)\ + f(x)&=2x dot (4x -1)\ + u(x)&=2x\ + u'(x)&=2\ + v(x)&=(4x-1)\ + v'(x)&=4\ + f'(x)&=2 dot (4x-1) + 2x dot 4\ + \ + b)\ + f(x)&=(5x+3) dot (x+2)\ + u(x)&=5x+3\ + u'(x)&=5\ + v(x)&=x+2\ + v'(x)&=1\ + f'(x)&=5 dot (x+2) + (5x+3) dot 1\ + \ + c)\ + f(x)&=(2-5x) dot (x +2)\ + u(x)&=2-5x\ + u'(x)&=5\ + v(x)&=x+2\ + v'(x)&=1\ + f'(x)&=5 dot (x+2) + (2-5x) dot 1\ + \ + d)\ + f(x)&=2x dot e^x\ + u(x)&=2x\ + u'(x)&=2\ + v(x)&=e^x\ + v'(x)&=e^x\ + f'(x)&=2 dot e^x + 2x dot e^x +$ + diff --git a/schule/mathe/pdfs/MA_2024-12-09.pdf b/schule/mathe/pdfs/MA_2024-12-09.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c3cf30ca4717c007dae36208dc56c7d9eaa1e5d2 GIT binary patch literal 28699 zcmce;1y~)+x-ANX;O-FI-QC^Y2@>4h-Q6`naCf)hnqa{RPH+htf(E@kleO>O`<->q zIq$sp-C5O4`tOpzYF2mG7^Au=l*J_(SQxqBC<1{G92^%hGqHoQH5@-b95FGIx|gFF zF_WZ&y(?%>&CS^Lw*h2k23bUnT+Bd6iJ8PzWR>1Z(uug*SlPQc*h>Q`oNdi4tc-2V z7*x$H+-!}U8Dvb&>|L!~y%?lHc_r*k989h3Er^-^-7aqCVq#`*YGm&UD%pitmm6?N zRsXj;4jT4WKrS<47G{tUPEZgINDA^74wUM@bX-hE98~E4%zuyvKmlrAF0N*FGWO;U z#J@WUumTOVa&dL`BBmAroH3&TQUX>bXHzq0Py?y|(ZIhBsJS^h+M3w`ok0xhMW7Kt zYLH)`raN0Xx;i)$^ZaffU>Dc=orp<`SQpf04puH=79eo5G83}`frFKkm<<$I*@;1c 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