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I. Differentiation – 1. Kontinuitet 20 eksisterer, hvis ∀ǫ > 0 ∃δ > 0 : (x − a) 2 + (y − b) 2 < δ ⇒ |f(x,y) − L| < ǫ 1.17. Ingen grænseværdi ☞ [S] 11.2 Limits and continuity Eksempel 1 f(x,y) = x2 − y 2 x 2 + y 2 har ingen grænseværdi for (x,y) → (0,0). Løsning f(x,0) = 1,x = 0 f(0,y) = −1,y = 0 1.18. Regneregler som forventet ☞ [S] 2.3 Calculating limits using the. . . Regneregler (1) Grænseværdien af en sum er summen af grænseværdierne. (2) Grænseværdien af en differens er differensen af grænseværdierne. (3) Grænseværdien af en konstant gange en funktion er konstanten gange grænseværdien. (4) Grænseværdien af et produkt er produktet af grænseværdierne.
I. Differentiation – 1. Kontinuitet 21 (5) Grænseværdien af en kvotient er kvotienten af grænseværdierne. 1.19. Kontinuitet på ny ☞ [S] 11.2 Limits and continuity 3 Definition Kontinuitet af f(x,y) i et punkt (a,b) skrives eller lim f(x,y) = f(a,b) (x,y)→(a,b) f(x,y) → f(a,b) for (x,y) → (a,b) f er kontinuert i D, hvis f er kontinuert i alle punkter (a,b) ∈ D.
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1. Grafiske/numeriske metoder IV Di
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Litteratur • Arnold, Ordinary dif
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