Example 8-5-17 - Maple Help

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Chapter 8: Infinite Sequences and Series

Section 8.5: Taylor Series

 

Example 8.5.17

a) 

Obtain p1x and p2x, degree 8 Maclaurin polynomials for fx=ex and gx=ln1+x, respectively.

b) 

Form the product p1p2.

c) 

Obtain the degree 11 Maclaurin polynomial for the product fxgx.

d) 

Obtain the first 10 coefficients cn formed from the Cauchy product of the coefficients of p1 and p2.

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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