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 589: 67



Work Step by Step

Since we have$$ 1-\frac{5^{3} x^{3}}{3 !}+\frac{5^{5} x^{5}}{5 !}-\frac{5^{7} x^{7}}{7 !}+\cdots\\ = 1-\frac{(5x)^{3}}{3 !}+\frac{(5x)^{5}}{5 !}-\frac{(5x)^{7}}{7 !}+\cdots\\ =1-5x+5x-\frac{(5x)^{3}}{3 !}+\frac{(5x)^{5}}{5 !}-\frac{(5x)^{7}}{7 !}+\cdots $$ Then by using Table 2, we see that this is a Maclaurin series of the function $$1-5x+\sin(5x).$$
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