   Chapter 4, Problem 18PS

Chapter
Section
Textbook Problem

Sine Integral Function The sine integral function Si ( x ) = ∫ 0 x sin t t d t is often used in engineering. The function f ( t ) = sin t t is not defined at t = 0, but its limit is 1 as t? 0. So, define f(0) = 1. Then f is continuous everywhere.(a) Use a graphing utility to graph Si(x).(b) At what values of x does Si(x) have relative maxima?(c) Find the coordinates of the first inflection point where x > 0.(d) Decide whether Si(x) has any horizontal asymptotes. If so, identify each.

(a)

To determine

To graph: The function Si(x)=0xsinttdt using a graphing utility.

Explanation

Given:

The function Si(x)=0xsinttdt

(b)

To determine

To calculate: The value of x where the function Si(x) has a relative maximum.

(c)

To determine

To calculate: The first inflection point for positive x for the function Si(x)=0xsinttdt.

(d)

To determine

To calculate: The horizontal asymptotes for the function Si(x)=0xsinttdt.

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