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 Taylor Series Suppose that f is a function whose domain includes the number a and suppose that f has derivatives of all orders at a. That is, suppose that f(n)(a) exists for all n. The power series is called the Taylor Series of f centered at a. In the case that a = 0, the Taylor Series is called the Maclaurin Series. Example: Find the Taylor series for f(x) = 1/x2 centered at a = 1. We have: f(x) = 1/x2                                so         f(1) = 1 f ′(x) = –2x–3                            so         f ′ (1) = –2(1)–3 = –2 f ″(x) = 6x–4                             so         f ″(1) = 6(1)–4 = 6 f (3) (x) = –24x–5                      so         f (3) (1) = –24(1)–5 = –24 f (4) (x) = 120x–6                      so         f (4) (1) = 120(1)–6 = 120 Therefore,   Online homework help for college and high school students. Get homework help and answers to your toughest questions in math, algebra, trigonometry, precalculus, calculus, physics. Homework assignments with step-by-step solutions.
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