Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 12 - Sequences and Series - 12.5 Taylor Series - 12.5 Exercises - Page 647: 4



Work Step by Step

We are given $f(x)=x^{5}e^{x}$ with $c=x^{5}$ for $r$ in $(-\infty,\infty)$ The Taylor series for $f(x)=x^{5}e^{x}$ is $f(x)=x^{5}.1+x^{5}.x+x^{5}\frac{1}{2!}x^{2}+...+\frac{1}{n!}x^n+...$ $=x^{5}+x^{6}+\frac{x^7}{2!}+...+\frac{x^{n+5}}{n!}+...$
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