Here is an alternative way to evaluate higher derivatives of a function f that may save time.

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Here is an alternative way to evaluate higher derivatives of a function f that may save time. Suppose you can find the Taylor series for f centered at the point a without evaluating derivatives (for example, from a known series). Explain why f(k) (a) = k! multiplied by the coefficient of (x - a)k. Use this idea to evaluate f(3) (0) and f(4) (0) for the following functions. Use known series and do not evaluate derivatives.

| f (x) = dt 1 + 14

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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