Example 8-5-17 - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

# Online Help

###### All Products    Maple    MapleSim



Chapter 8: Infinite Sequences and Series



Section 8.5: Taylor Series

Example 8.5.17



 a) Obtain ${p}_{1}\left(x\right)$ and ${p}_{2}\left(x\right)$, degree 8 Maclaurin polynomials for $f\left(x\right)={e}^{x}$ and $g\left(x\right)=\mathrm{ln}\left(1+x\right)$, respectively.
 b) Form the product ${p}_{1}\cdot {p}_{2}$.
 c) Obtain the degree 11 Maclaurin polynomial for the product $f\left(x\right)\cdot g\left(x\right)$.
 d) Obtain the first 10 coefficients ${c}_{n}$ formed from the Cauchy product of the coefficients of ${p}_{1}$ and ${p}_{2}$.
 e) Observe that the coefficients formed from the Cauchy product (Theorem 8.2.4) are always correct, but those formed from the product of the polynomials are correct only to a limited degree in $x$.







© Maplesoft, a division of Waterloo Maple Inc., 2023. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.

For more information on Maplesoft products and services, visit www.maplesoft.com