Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - 11.7 Taylor Series - Exercises - Page 588: 2


$$f(x)= =1+2(x-3)+6(x-3)^2+\frac{1}{2}(x-c)^3+..$$

Work Step by Step

The first four terms of the Taylor series of $ f (x)$ centered at $c = 3$ are: $$f(x)=f(c)+f'(c)(x-c)+f''(c)(x-c)^2/2!+f'''(c)(x-c)^3/3!+...\\ =1+2(x-3)+6(x-3)^2+\frac{1}{2}(x-c)^3+..$$
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