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: 65



Work Step by Step

Since we have$$ 1+x^{3}+\frac{x^{6}}{2 !}+\frac{x^{9}}{3 !}+\frac{x^{12}}{4 !}+\cdots\\ =1+x^{3}+\frac{(x^{3})^{2}}{2 !}+\frac{(x^{3})^{3}}{3 !}+\frac{(x^{3})^{4}}{4 !}+\cdots\\ $$ Then by using Table 2, we see that this is Maclaurin series of the function $$e^{x^3}.$$
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