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Wichtige Formeln und Regeln für die Analysis

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Uploaded on
December 17, 2023
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Written in
2022/2023
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Dreiecksungleichung Wurzelkriterium




ma aber
|a + b| = (a) + 1b) ,
(2 + w((z | + (w) ,
(z + w(z((z) -
wi

Bernoullische
Ungleichung
(1 + x)21 + nx


Teleskopsumme Quotientenkriterium
&
Im mybsn
(an-an-) =
An-am--
k= m



Gauß
k =
+)
4n
u= 0
2


Endliche Summe Satz Mertens
geom .
von



= zww abs .
Konv
.

abs
an

Konr =
und
konba n
beide .
Produkt abs .
konv.




= abs .
Kon




Binomischer Lehrsatz en
: im
(a+ blu
= a


Reite =,
I
cosl-x1 = coSX
gerade


auchy-Schwarzunpeiche,
Cost =
Z



sinx Im ein sinix = -


sinx
unger
= .


tanx =
Sin X


Grenzwerte eix = cosx + isinx




oh
(1 + (2) + 1

(7 +
m + 1
-
x24 +1



124+ 1) !
( +
(= Bernoulli
1 +
E = 1+ m + 2


( +=) = 1+ = =
2 -> 2

(1 + =( + ex
Stetige Funktionen
Häufungspunkt
a 1 FEc0760 zeM IzS Ifl-sk
limflzls
>
-
: =
,


nu
= 0
en
bei fal IVESO
Los & stetig a falls limf(z ZEM , -als
=
- ,
:




(f(2) f(a)))
e
=> -




f stetig auf M , falls stetig auf allen afM




geometrische Reihe


konv für



Leibniz-Kriterium

(anlnemt
= ak konvergiert

* an konv .
=(an) Nullfolge
n = r




an divergiert =lau) keine
Nullfolgein

Cachyscher Verdichtungssatz
an0 ,
Kult an
konv kon
Dirichlereihe

konv .
de
falls

Absolute
konvergenz
aul konverpentin
Majoranten- , Minorantenkriterium
~bu
=a kon
lauledn konv.
h= m
N

laulbu
~Ebn di
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