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Jonas Hahn
2025-06-11 20:52:38 +02:00
parent b622377bb2
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S2/DiffII/Zettel/Zettel8.typ Normal file
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= Aufgabe 3
Angenommen $f: U -> W_(1) times W_(2) $ ist diffbar in $a$. Dann wissen wir
$
lim_(h -> 0) (f (a + h) - f (a)) / (norm(h)) = 0.
$
Mit der Norm auf $W_1 times W_2 $ und der Definition von $f = (f_1, f_2 )$ folgt dann
$
lim_(h -> 0) ((f_1 (a + h), f_2 (a + h)) - (f_1 (a), f_2 (a))) / (norm(h_1) + norm(h_2 ) ) = 0
$