Example 8-5-17 - Maple Help



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 $x$.







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