From c71fc38ac310444535bc3e28b0419dc1c1736c4f Mon Sep 17 00:00:00 2001 From: Erik Grobecker Date: Mon, 30 Sep 2024 14:08:43 +0200 Subject: [PATCH] Mathe am 30.09.2024 --- mathe/MA_2024-09-30.typ | 107 ++++++++++++++++++ ...r der Vertragstheorie Hayek.excalidraw.png | Bin 0 -> 107179 bytes template.typ | 2 +- 3 files changed, 108 insertions(+), 1 deletion(-) create mode 100644 mathe/MA_2024-09-30.typ create mode 100644 philosophie/assets/PL_Struktur der Vertragstheorie Hayek.excalidraw.png diff --git a/mathe/MA_2024-09-30.typ b/mathe/MA_2024-09-30.typ new file mode 100644 index 0000000..72ece9b --- /dev/null +++ b/mathe/MA_2024-09-30.typ @@ -0,0 +1,107 @@ +#import "../template.typ": apply-template +#show: apply-template +#set page(header: [Mathe am 30.09.2024]) + +#outline() + += Exponentialfunktionen + +== S. 101 Nr. 7 + +=== a) + +// $1 dot 0.4^x$ + +$ +f(x)&=1 dot 0.75^(x/1.8)=(0.75^(1/1.8))^x=0.8523^x +$ + +$1$ → 100% Lichtintensität\ +$0.75$ → 75% Lichtintensität\ +$1.8$ → 1,80m Tiefe + +*Aufgabe:* Bis zur nächsten Stunde erklären können wie man zu dieser Formel kommt + +=== b) + +$ +f(0.6)&=0.8523^0.6 &approx 0.91\ +f(3.5)&=0.8523^3.5 &approx 0.57\ +f(9)&=0.8523^9 &approx 0.23 +$ + +=== c) + +$ +// wo kommt die 0.01 her???? +log_0.8523 (0.01)&=x\ +28.82 &approx x +$ + +Ab einer Tiefe unter ca. $28.82$m ist die Lichtintensität auf unter 1% gesunken. + +== HA + ++ S. 101 Nr. 7a) erklären können ++ S. 102 Nr. 8 und Nr. 11 + +== Exponentialfunktionen ableiten + +$ +f(x)&=a^x\ +f'(x)&=f'(0) dot a^x\ +"Beispiel:"\ +f(x)&=2^x & (a>0) \ +f'(x)&=1 dot 2^x\ + +"Nebenrechung:"\ +f(0)&=2^0=1\ +f'(0)&=1 +$ + +// #table( +// columns: (auto,auto), +// table.header( +// [$f(x)$], [$f'(0)$], +// ), +// [$$], [], +// [$$], [], +// [$$], [], +// [$$], [], +// [$$], [], +// [$$], [], +// ) + +=== Wiederholung: Ganzrationale Funktionen + +$ +f(x)&=x^n\ +f'(x)&=n dot x^(n-1)\ +\ +f(x)&=x^n+x^m\ +f'(x)&=n dot x^(n-1) + m dot x^(m-1) +$ + +== $e$-Funktionen + +$ +f(x)=e^x\ +e approx 2.71828... +$ + +=== S. 105 Nr. 1 +*a):* +$ +f(x)&=e^x+1\ +f'(x)&=e^x +$ +*b):* +$ +f(x)&=e^x+x\ +f'(x)&=e^x+1 +$ +*c):* +$ +f(x)&=e^x+2x²\ +f'(x)&=e^x+4x +$ diff --git a/philosophie/assets/PL_Struktur der Vertragstheorie Hayek.excalidraw.png b/philosophie/assets/PL_Struktur der Vertragstheorie Hayek.excalidraw.png new file mode 100644 index 0000000000000000000000000000000000000000..5f50293e72bfb6d5da693eb9a8de5285fb4a297f GIT binary patch literal 107179 zcmeFZWmr`G|L-et!_Y%_w=^m_bW5sq$;1{siqz3kA;6`e^5S5_xr&ErUz<@a=I|{omT7&UM2GSmn4`<3E7^yvL0YLSvEB+a<+%! zxT?cyXlVW7*z8;^@7}5oCq0TtdSv?UovQxbpZd0nvywTD&CDD`PEO#+@%+YO^PHL4 zt-g=fWW})fY3PXb^-lE%HCc3$gtwS%OlUZ&|MlkwCG?j%hOZJc!qxxl)&Kmdh>oi+ z4f>zHDU0q*415#sJ?H=Y(_Fll`2T&S|NLf+k}UKKpA&-Z|9LC_{J@9GwMYN2oBZcH zqZDYNAL}Z8lm53+{QUuB(#ZclzWaA%O)$yQW|6I{M6GoV$X)HM6#~-w5tETgqu`o?d55Jyb)sYFTsw*7;(^5B#J|x<{>Q|ourJpa@^Z)j^S`<(z&c9QIj7&C!WqMYZdMtg z6Q7?!cfR%#s`EEmUmz*lbm}4Uk=`@VaM%sCT{iKr_pWVq6;essY$~01*ZYiMG5)5_ 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