fixed integrierbar bedinung
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@@ -163,26 +163,17 @@
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- Beweiße: durch Induktion
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- Beweiße: Hat min. ein konvergent Teilefolge
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- (Beweiße: Ungleichung $abs(a_n) <= k$)
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*Monoton fallend/steigended*
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*Monoton fallend/steigended $a_(n+1) lt.eq.gt a_(n)$*
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- Beweise: Induktion
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#grid(columns: (1fr, 1fr),
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inset: 0.2mm,
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align(top+center, [*Fallend*]), align(top+center, [*Steigend*]),
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[$ a_(n+1) <= a_(n), quad a_(n+1) >= a_(n) $],
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[$ a_(n+1)/a_(n) < 1, quad a_(n+1)/a_(n) > 1 $],
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)
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*Konvergentz Allgemein*
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$lim_(n -> infinity) a_n = a$
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$forall epsilon > 0 space exists n_epsilon in NN$ sodass \
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- Konvergent $-> a$: $a_n in [a - epsilon, a + epsilon] $
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- Divergent $-> infinity$: $a_n in [epsilon, infinity) $
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- Divergent $-> infinity$: $a_n in (-infinity, epsilon) $
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$space forall n > n_epsilon$
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- unbeschränkt $=>$ Divergent
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*Konvergentz Häufungspunkte*
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- $a_n -> a <=>$ Alle Teilfolgen $-> a$
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@@ -579,7 +570,7 @@
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#bgBlock(fill: colorIntegral, [
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#subHeading(fill: colorIntegral, [Integral])
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Wenn $f(x)$ stetig und monoton $=>$ integrierbar
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Wenn $f(x)$ stetig oder monoton $=>$ integrierbar
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Summen: $integral f(x) + g(x) d x = integral f(x) d x + integral g(x)$
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