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Lecture notes

25. Vl Ana1LinA Anwendungen der Taylorapproximation

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Dies ist eine vollständige Vorlesungsmitschrift zur 25. Vorlesung des Moduls Analysis I und lineare Algebra für Ingenieurswissenschaften. In dieser Vorlesung werden Anwendungsfälle der Taylorapproximation thematisiert. Dazu gehören auch die Fehlerabschätzung, Approximation mit vorgegebener Genauigkeit, die Taylorreihe und die Erklärung der Eulerformel mithilfe der Taylorapproximation.

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Uploaded on
February 1, 2023
Number of pages
5
Written in
2022/2023
Type
Lecture notes
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Penn-karras
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Näherungsweise Berechnung von Funktionswerten

Bsp 1 Was istV47 Taylor n Z 4
444
f F f L



fkk IE Es f 4 Z

T.lxl EIYIK x.IE EGLIA 4 FIA 4 SIE 4 LIEGT
2 EA 4 FG 45
54,4 f 4,412T 4,41 2 714,4 41 4,4 4

2 2 0,4 74 0,42 2 0,1 94
2,1 04
2,1 0.0025

2,0972
zwischen 4 und 4,4
Rz ZEIT x 4,3
4 3 4,4

IT G 4
Ej Gesacktobere sohu.a
für KAI
R44t Ef gg e.gg
Rf4,4 tYsY S E aoonzs

V44 E 2,097570,000125

, Bsp Exp FA

GA E FEI GG GG O
f O 1

T.AZE.SI E EE FETT.EE
F4 EoE
RCxkeE E IKItRGI 1tx Ete E strengmonoton wachs
E o
1 2 te te 1 1
EeJoe für 0
5 2 7 EZ E Gebet 1 3 O
o o e El
Select
Zine
Approximation mit vorgegebenen Genauigkeit

Bsp er soll im Intervall 1,1 approximiertwerden mit einer Genauigkeit
von 0,00001 10 5
OE EX El 1 5 1
3 0
e e e es



IR.AT EjI EEIseE E
5
z.B v8 R L 10

Fehlerabschätzung


fl x flx.ltflx.lk xd Rkk the xD
TG
flxl flx.ltflx.lk ol flxl flx.ltfk.IG x.lt EA
x x x Xo Ax x. Ax
flx.tAxlzflx.ltflx.l Axflx.tt fCx.tf'lx.tAxttIIIAy
Af flxottxl flxolzflx.l.AXAf flx.l.Axtfj.AT
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