From fba26a8ea87873df8ef3bb1ee8e30fe300f96aaf Mon Sep 17 00:00:00 2001 From: Erik Grobecker Date: Tue, 10 Dec 2024 10:03:41 +0100 Subject: [PATCH] Mathe am 05.12.2024 --- INDEX.md | 1 + schule/mathe/MA_2024-12-05.typ | 142 ++++++++++++++++++++++++++++ schule/mathe/pdfs/MA_2024-12-05.pdf | Bin 0 -> 21968 bytes 3 files changed, 143 insertions(+) create mode 100644 schule/mathe/MA_2024-12-05.typ create mode 100644 schule/mathe/pdfs/MA_2024-12-05.pdf diff --git a/INDEX.md b/INDEX.md index a70e528..724c59b 100644 --- a/INDEX.md +++ b/INDEX.md @@ -93,6 +93,7 @@ | | 28.10.2024 | [hier](./schule/mathe/pdfs/MA_2024-10-28.pdf) | | | 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) | Zusammenfassungen: diff --git a/schule/mathe/MA_2024-12-05.typ b/schule/mathe/MA_2024-12-05.typ new file mode 100644 index 0000000..c11e8fc --- /dev/null +++ b/schule/mathe/MA_2024-12-05.typ @@ -0,0 +1,142 @@ +#import "@preview/grape-suite:1.0.0": exercise +#import exercise: project, task, subtask + +#set text(lang: "de") + +#show: project.with( + title: [Stunde nach der Klausur], + seminar: [Mathe Q2], + // show-outline: true, + author: "Erik Grobecker", + date: datetime(day: 5, month: 12, year: 2024), +) + +#show rect: set align(center) + += Irgendeine HA +*S. 113 Nr. 2a)* + +#rect($ + f(x)&=90 dot 0.87^x && |:90 \ + 0.5&=0.87^x && | log_(0.87)\ + x &= log_(0.87)(0.5)\ + x &= 4.87 +$) + +*b)* +$09 dot 0.87^10 = 22.36$\ +Er hat nach 10 Jahren eine Wachstumsgeschwindigkeit von ca. 22,36 cm pro Jahr. + +*c)* +#rect($ + 50 &= 90 dot 0.87^x &&|:90 \ + 5/9 &= 0.87^x &&|log \ + x &= log_(0.87)(5/9) +$) + +*d)* +#rect($ + f(x)&=90 dot 0.87^x \ + F(x)&=90/ln(0.87) dot 0.87^x +$) + +*e)* +#rect($ + integral_0^10 f(x) d x & #sym.tilde.eq 575.71 +$) + +*f)* +#rect($ + integral_0^20 f(x) d x &= 606\ + 606 + 90 &= 696 +$) + +*g)* +#rect($ + 606:20 &= 30.3 +$) + += Hausaufgabe zur nächsten Stunde +S. 133 Nr. 1 & 2 + +== Nr. 1 + +$ + u(x) &= x^2\ + v(x) &= x+2\ + w(x) &= sqrt(x) +$ + +$u+v$:\ + +$ + x^2 + (x+2) +$ + +$u dot v$:\ + +$ + x^2 dot (x + 2) = x^3 + 2x^2 +$ + +$u circle.tiny v$: + +$ + u(v(x))\ + u(x+2)\ + (x+2)^2\ + x^2 + 4 +$ + +$w dot v$ + +$ + sqrt(x) dot (x+2)\ + sqrt(x) dot x + 2 dot sqrt(x) +$ + +$w circle.tiny v$: + +$ + w(v(x))\ + w(x+2)\ + sqrt(x+2) +$ + +== Nr. 2 + +=== a) + +$ + f(x) &= (2x -3)^2\ + "Summe:"\ + f(x)&=(2x -3)^2\ + &=(a+b)^2\ + &=a^2 + 2a b + b^2\ + &= 2x² + (2 dot (2x-3)) + (-3^2)\ + &= 2x² + (4x - 6) + 9\ + \ + "Produkt:"\ + f(x) &= (2x-3)^2\ + &= (2x-3) dot (2x-3)\ + \ + "Kette:"\ + f(x) &= (2x-3)^2\ + g(u) &= u²\ + h(x) &= 2x-3\ + g(u(x)) &= (u(x))²\ + &= (2x-3)^2 +$ + +=== b) + +$ + g(x) &= 2 dot e^(3x) -> "ist Produkt"\ + \ + "Kettenregel:"\ + g(u) &= 2 dot e^u\ + u (x) &= 3x\ + g(x) &= g(u(x))\ + &= 2 dot e^(u(x))\ + &= 2 dot e^(3x) +$ 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