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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 9.4 - Problem 72e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 9.4 - Problem 72e

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# Sine integral function The function is called the sine

ISBN: 9780321570567 2

## Solution for problem 72E Chapter 9.4

Calculus: Early Transcendentals | 1st Edition

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Problem 72E

Problem 72E

Sine integral function The function  is called the sine integral function.

a. Expand the integrand in a Taylor series about 0.

b. Integrate the series to find a Taylor series for Si.

c. Approximate Si (0.5) and Si (1). Use enough terms of the series so the error in the approximation does not exceed 10−3

Step-by-Step Solution:

Solution 72E:

Step 1:

Given , the function “Si(x) =  dt” is called the sine integral function.

Integrand is ;

1. In this problem we need to expand the  integrand in a taylor series about “0”.

We know that the taylor series about “0” is ;

f(x) = f(0) +x ++................

Consider , f(t) =  , then f(0) =  = 1

, then = 0

= , then   = -1, since = = -1

= , then   = 0

= , then  = 1, since = = 1

……………………………………

Therefore , the taylor series about zero is ;

f(t) =  =  1 +t ++................

= 1 - +-................

Step 2 of 4

Step 3 of 4

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