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III. Potensrækker – 1. l’Hospitals regel og uegentlige integraler 250 ✌ Sammenligning 1.2. Ubestemt udtryk ☞ [S] 4.5 Indeterminate forms and l’Hospital’s rule Eksempler Ubestemte udtryk ln(x) 1 lim x→1 x − 1 ln(x) 2 lim x→∞ x − 1 1.3. Ubestemt 0-0 udtryk ☞ [S] 4.5 Indeterminate forms and l’Hospital’s . . . Definition Lad f(x) → 0,g(x) → 0 når x → a. Udtrykket kaldes ubestemt af form 0 0 . Eksempel f(x) lim x→a g(x) lim x→1 x 2 − 1 x − 1
III. Potensrækker – 1. l’Hospitals regel og uegentlige integraler 251 er ubestemt af form 0 0 . 1.4. Ubestemt udtryk ☞ [S] 4.5 Indeterminate forms and l’Hospital’s rule Definition Lad f(x) → ∞,g(x) → ∞ når x → a. Udtrykket kaldes ubestemt af form ∞ ∞ . Eksempel er ubestemt af form ∞ ∞ . f(x) lim x→a g(x) ln |x| lim x→0 x−1 1.5. l’Hospitals regel 1 ☞ [S] 4.5 Indeterminate forms and l’Hospital’s rule Sætning (l’Hospitals regel) Antag, at f,g er differentiable og g ′ (x) = 0 for x = a tilpas nœr a. Hvis f(x) lim x→a g(x) er et ubestemt udtryk af form 0 0 , så er f(x) f lim = lim x→a g(x) x→a ′ (x) g ′ (x)
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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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V. Matricer - 4. Determinanter = (
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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