Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 11 - Infinite Sequences and Series - 11.10 Exercises - Page 790: 62

Answer

$x+\frac{x^{2}}{2}+\frac{x^{3}}{3}+...$

Work Step by Step

$y=e^{x}ln(1+x)$ $ln(1+x)=x-\frac{x^{2}}{2}+\frac{x^{3}}{3}+....+\frac{x^{n}}{n}$ and $e^{x}=1+x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+...$ $e^{x}ln(1+x)=(1+x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+..)(x-\frac{x^{2}}{2}+\frac{x^{3}}{3}+....+\frac{x^{n}}{n})$ $\approx x+\frac{x^{2}}{2}+\frac{x^{3}}{3}+...$
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