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

Question:

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.

eх sin t? dt f (x)

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

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

Question Posted: