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III. Potensrækker – 3. Potensrækker 290 3.21. Gentagen differentiation ☞ [S] 8.7 Taylor and Maclaurin series Udregning - fortsat f (n) (0) = n! · cn eller cn = f(n) (0) n! 3.22. MacLaurin ☞ [S] 8.7 Taylor and Maclaurin series Observation f(x) = c0 + c1x + c2x 2 + c3x 3 + ... kan skrives eller f(x) = f(0) + f ′ (0)x + f ′′ (0) 2! x2 + f ′′′ (0) 3! x3 + ... f(x) = ∞ n=0 f (n) (0) x n! n 3.23. Taylor-udvikling, centrum a ☞ [S] 8.7 Taylor and Maclaurin series Observation f(x) = c0 + c1(x − a) + c2(x − a) 2 + c3(x − a) 3 + ...
III. Potensrækker – 3. Potensrækker 291 kan skrives eller f(x) = f(a) + f ′ (a)(x − a) + f ′′ (a) 2! f(x) = ∞ n=0 (x − a) 2 + f ′′′ (a) (x − a) 3! 3 + ... f (n) (a) (x − a) n! n (“Taylor-rækken for f med centrum i a”, eller “Taylor-udviklingen af f ud fra a”) 3.24. Koefficienter ☞ [S] 8.7 Taylor and Maclaurin series 5 Sætning Hvis en potensrœkke med centrum i a har konvergensradius R > 0, så har sumfunktionen ∞ f(x) = cn(x − a) n koefficienter n=0 cn = f(n) (a) n! 3.25. Taylorrække ☞ [S] 8.7 Taylor and Maclaurin series Definition
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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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