# Finanzmathematik by Kirsten Wüst

By Kirsten Wüst

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22:ȱ log a 1 5 , ȱdennȱ 2 5 32. ȱ 2 , ȱdennȱ 3 2 1 32 x , ȱdennȱ a x 0 , ȱdennȱ a 0 ax . ȱ 1. ȱ Soȱ nenntȱ manȱ denȱ Logarithmusȱ zurȱ Basisȱ aȱ =ȱ 10ȱ denȱ dekadischenȱLogarithmusȱundȱschreibtȱoftȱȱ lg( x) log 10 ( x). ȱDenȱLogarithmusȱzurȱBasisȱaȱ=ȱeȱbezeichnetȱmanȱalsȱ natürlichenȱLogarithmusȱ undȱschreibtȱȱ ln( x) log e ( x). ȱ Beiȱ denȱ anderenȱ Logarithmenȱ gehenȱ wirȱ davonȱ aus,ȱ dassȱ dasȱ „Mitführen“ȱ derȱBasisȱdieȱLesbarkeitȱderȱLogarithmenȱerhöht. 9 Logarithmusgesetze AusȱdenȱPotenzgesetzenȱlassenȱsichȱeineȱReiheȱvonȱLogarithmusgesetzenȱableiten:ȱȱ 1.

6:ȱ xa  (  b ) 75 73 xa  b . ȱ 7 5  7 3 72 49. 8)ȱ ȱ 5. ȱEsȱlässtȱsichȱschreibenȱ x a b a a x  x  xa  xa  x  a  a  a   a b  mal xa  b . 3 3 22  22  22 22  2 2 2 3 2 2 6. h. ȱ Gesuchtȱ istȱ alsoȱ dasȱ y,ȱ fürȱ das y 3 8. Esȱgiltȱhierȱnatürlichȱyȱ=ȱ2,ȱdenn 2 3 8. ȱ Mitȱ derȱ eingeführtenȱ SchreibweiseȱresultiertȱdiesesȱausȱdenȱPotenzgesetzen:ȱ 1 ( n x )n ( x n )n x. ȱ 1. ȱ Dieȱ c ȱhatȱdaherȱgenauȱzweiȱreelleȱLösungenȱ x1 / 2 Fürȱ cȱ =ȱ 0ȱ berührtȱ dieȱ Funktionȱ y rn c . ȱDieȱGleichungȱ x n nurȱeineȱreelleȱLösungȱ x 0.

30)ȱ j 1 3. n n n j 1 j 1 j 1  a j   b j  a j  b j. ȱ AlsȱSchreibweisenȱfürȱeineȱFolgeȱexistieren:ȱȱ (a n ) (a n ) n 1, 2 ,... (a n )nN ȱoderȱauchȱ {a n } {a n }n 1, 2 ,... 48: (a n ) 2 1, n n 1 1 1 , , , .... ȱȱ ȱ 2 3 4 ȱ ȱ ȱ ȱȱȱȱȱȱȱȱȱƑȱ 1, 1, 1, 1, ... ȱ ȱ ȱ ȱ ȱȱȱȱȱȱȱȱȱƑ ȱ ȱ ȱ ȱȱȱȱȱȱȱȱȱƑȱȱ 2 , 4 , 8 , 16 , ... ȱ an  1 ! ȱ ȱ WichtigeȱGrenzwerteȱ WirȱwollenȱhierȱnurȱzweiȱbesondersȱwichtigeȱGrenzwerteȱnäherȱbetrachten:ȱ 1. Fürȱjedesȱreelleȱcȱ>ȱ0ȱgiltȱ 1 o 0. ȱ 1, 1 / 2 , 1 / 3 , 1 / 2 ,...

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