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