Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 11 - Infinite Sequences and Series - 11.10 Taylor and Maclaurin Series - 11.10 Exercises - Page 812: 70

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

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.