Power series representing ∫sinx/x

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To find the power series representing g(x) = ∫sin(x)/x, start with the Maclaurin series for sin(x), which is sin(x) = x - (x^3/3!) + (x^5/5!) - (x^7/7!). Divide this series by x to obtain the series for sin(x)/x. Then, integrate the resulting series term by term to derive the power series for g(x). This method effectively utilizes the properties of power series and integration to solve the problem. The approach is confirmed as correct by participants in the discussion.
Ryantruran
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Homework Statement



Find the Power Series representing
g(x)=∫sin(x)/x


Homework Equations



sin(x)= x-(x^3/3!)+(x^5/5!)-(x^7/7!)


The Attempt at a Solution



I Havent attempted yet but was wondering if you start with the maclaurin series of sin(x)
then divide everything by x then integrate the entire summation
 
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Ryantruran said:

Homework Statement



Find the Power Series representing
g(x)=∫sin(x)/x


Homework Equations



sin(x)= x-(x^3/3!)+(x^5/5!)-(x^7/7!)


The Attempt at a Solution



I Havent attempted yet but was wondering if you start with the maclaurin series of sin(x)
then divide everything by x then integrate the entire summation
Yes, that's what you do.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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