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Chapter 8: Q 29 (page 704)

Use the Maclaurin series for exto find power series representations

for g(x)=x2ex,g'(x)and 鈭�g(x)dx

Short Answer

Expert verified

The power series representation forg(x)=x2exisg(x)=鈭�k=0鈭�1k!xk+2

Step by step solution

01

Given information

The function isf(x)=ex

02

Find the Maclaurin series for the function

The Maclaurin series for the function f(x)=exis

1+x+12!x2+13!x3+14!x4+鈥�

Or f(x)=鈭�k=0鈭�1k!xk

Hence, g(x)=x2ex

g(x)=x2鈭�k=081k!xk=鈭�k=081k!xk+2

03

Find the power series representation for g(x)=x2ex 

The power series representation for g(x)=x2exis

g(x)=x2鈭�k=0鈭�1k!xk

g(x)=鈭�k=0鈭�1k!xk+2

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