Power Series expansion of hyperbolic functions

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Homework Help Overview

The discussion revolves around the power series expansion of the expression \(\frac{\cosh x}{\sinh x} - \frac{1}{x}\), focusing on the hyperbolic functions involved.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss simplifications of the expression and question the validity of those steps. There are inquiries about expanding the hyperbolic functions and the implications of the \(1/x\) term in the context of series expansion.

Discussion Status

The conversation is ongoing, with participants providing feedback on simplifications and suggesting further steps, such as expanding the hyperbolic functions and considering Taylor series. There is no explicit consensus yet, but several lines of reasoning are being explored.

Contextual Notes

Participants are navigating potential typos and simplification errors, which may affect the clarity of the problem setup. The discussion reflects a typical homework scenario where assumptions and methods are being questioned.

thanksie037
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Homework Statement



power series expansion of:

((cosh x)/(sinh x)) - (1/x)


Homework Equations



cosh x = (1/2)(ex + e-x)
sinh x = (1/2)(ex - e-x)

The Attempt at a Solution


what i have so far:

I simplified the first part of the eq to read :
e2x-1
e2x-1


now I am stuck. please help
 
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You simplified for it to be [tex]\frac{e^{2x}-1}{e^{2x}-1}[/tex]? Isn't that just 1?
 
error in simplification:

[tex]\frac{e^{2x}+1}{e^{2x}-1}[/tex]
 
I'm sorry that was a typo. Should I just expand both was like you would ex? how about the 1/x part?
 
I would and then hopefully things will cancel, for example what's the expansion for [tex]e^{2x} - 1[/tex]?
 
How do one usually find the taylor series of a given function?
now you have a function, what do you do? :rolleyes:
 

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