Calculus 8th Edition

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

Chapter 11 - Infinite Sequences and Series - 11.11 Application of Taylor Polynomials - 11.11 Exercises - Page 821: 25


Four terms

Work Step by Step

We are given that $f(x)=e^x$ and $f^n(x)=e^x$ Check the Taylor inequality at $x=0.1$ Since, we have $|R_n(x)|\leq \dfrac{M}{(n+1)!}|x-a|^{n+1}$ This gives: $|R_2(x)|\leq \dfrac{e^{(0.1)}}{(2+1)!}|0.1-0|^{(2+1)}\approx 0.0002$ and $|R_3(x)|\leq \dfrac{e^{(0.1)}}{(3+1)!}|0.1-0|^{(3+1)}\approx 0.000005$ It has been seen that the remainder $|R_3(x)| \lt 0.00001$ require four terms.
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.