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I. Differentiation – 7. Lagrangemetoden 154 I alt er der 5 punkter at tabellægge (a,b) (0,0) (−1,0) (1,0) (0, −1) (0,1) f(a,b) 0 1 1 2 2 På cirkelskiven D er absolut maksimumspunkt og -værdi: f(0, ±1) = 2 absolut minimumspunkt og -værdi: f(0,0) = 0 7.25. Find mindste afstand ☞ [S] 11.8 Lagrange multipliers Eksempel 4 Bestem punkter på kugleskallen x 2 + y 2 + z 2 = 4 som er nærmest og længst fra punktet (3,1, −1).
I. Differentiation – 7. Lagrangemetoden 155 z x 2 (3,1, 1) 7.26. Find mindste afstand ☞ [S] 11.8 Lagrange multipliers Eksempel 4 Bestem ekstremumsværdier af under bibetingelsen f(x,y,z) = (x,y,z) − (3,1, −1) 2 = (x − 3) 2 + (y − 1) 2 + (z + 1) 2 g(x,y,z) = x 2 + y 2 + z 2 = 4 7.27. Find mindste afstand ☞ [S] 11.8 Lagrange multipliers y
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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Forord "Slides" til forelæsningern
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I. Differentiation - 1. Kontinuitet
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1. Grafiske/numeriske metoder IV Di
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1. Vektorer og matricer V Matricer
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V. Matricer - 4. Determinanter 419
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V. Matricer - 4. Determinanter = (
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1. Egenvektorer VI Egenvektorer og
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VI. Egenvektorer og diagonalisering
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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Identitetsmatricen, 383 Identitetsm
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etningsafledede, 89, 102 retningsfe
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