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I. Differentiation – 1. Kontinuitet 24 er kontinuerte. (3) Funktionsudtryk er kontinuerte, hvor de er definerede. 1.24. Anvend regler ☞ [S] 11.2 Limits and continuity Eksempler om kontinuitet (1) Kontinuert på R 2 (2) Kontinuert på R 2 ,x = pπ (3) Kontinuert når x 2 + y 2 > 2 x − y x 2 + y 2 + 1 cos y sin x ln(x 2 + y 2 − 2) 1.25. Kontinuert de rigtige steder ☞ [S] 11.2 Limits and continuity Eksempel 1, 6, 7 g(x,y) = x 2 −y 2 x 2 +y 2 , (x,y) = (0,0) 0, (x,y) = 0 er ikke kontinuert i (0,0), da g(x,y) ingen grænseværdi har for (x,y) → (0,0).
I. Differentiation – 1. Kontinuitet 25 Fra regneregler for kontinuitet følger, at g(x,y) er kontinuert på mængden R 2 \{(0,0)} af alle talpar fraregnet (0,0). 1.26. Hul i taget ☞ [S] 11.2 Limits and continuity Figur z x y Ikke kontinuert i (0,0) 1.27. Øvelse ☞ [S] 11.2 Limits and continuity
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V. Matricer - 4. Determinanter = (
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Litteratur • Arnold, Ordinary dif
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