Represent sinh2x as power series

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Homework Help Overview

The discussion revolves around finding a power series representation for the function f(x) = sinh(2x). Participants are exploring how to derive the first three non-zero terms of this series.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Some participants suggest substituting 2x into the series for sinh(x) directly. Others discuss the use of Taylor series and differentiation as methods to derive the series.

Discussion Status

There appears to be a general agreement on the approach of substituting and using Taylor series, with some participants expressing satisfaction with their methods. However, no explicit consensus on a single approach has been reached.

Contextual Notes

One participant mentions a previous mistake on a test related to not having the formula available, indicating that there may be constraints regarding the use of reference materials in homework settings.

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Homework Statement



find the first three non zero terms of a power series representation of f(x)= sinh 2x

Homework Equations



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The Attempt at a Solution



seems easy enough do I just substitute 2x for x?

so sinh 2x= 2x + 8x3/3! + 32x5/5!
 
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Yes that should be correct.
 
Thanks I messed this one up on a test because I forgot to put the formula on my cheat sheet but damn that was easy
 
You didn't really need to have the formula on your cheat sheet if you know how to differentiate sinh(2x). Just use the general formula for a Taylor series.
 
Dick said:
You didn't really need to have the formula on your cheat sheet if you know how to differentiate sinh(2x). Just use the general formula for a Taylor series.

Or if you know how to express sinh(x) in terms of exponentials, and you know the Taylor series for exp(x).
 
Well I tried using Taylor series and am happy to say that was also very easy and much more satisfying. Those Taylor series aren't so bad after all:)
 

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