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

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Derivative trick Here is an alternative way to evaluate higher derivatives of a function ƒ that may save time. Suppose you can find the Taylor series for ƒ centered at the point a without evaluating derivatives (for example, from a known series). Then ƒ(k)(a) = k! multiplied by the coefficient of (x - a)k. Use this idea to evaluate ƒ(3)(0) and ƒ(4)(0) for the following functions. Use known series and do not evaluate derivatives.

ƒ(x) = ecos x

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