Finding Power Series Representation of Derivatives: 1/x-9

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Discussion Overview

The discussion centers on finding a power series representation for the derivative of the function \(1/(x-9)\). The scope includes mathematical reasoning and exploration of series expansions.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant suggests using the Taylor series around \(a=0\) to find an approximation, mentioning the need to calculate derivatives up to the desired accuracy.
  • Another participant points out a potential typo in the original function, noting that \(1/x\) is infinite at \(x=0\).
  • A later reply clarifies the intended function as \(1/(x-9)\) and proposes rewriting the expression as \(-1/9 \cdot d/dx (1/(1-x/9))\), hinting at the use of geometric series for further analysis.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are differing interpretations of the original function and its representation.

Contextual Notes

There are unresolved assumptions regarding the choice of point for the Taylor series expansion and the implications of the function's behavior at specific values.

sportlover36
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how can i find a power series representaion of d/dx (1/x-9)
 
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You can find an approximation by calculating the Taylor series around some point (a=0 would probably be easiest). All you need to do is find derivatives of the function up to the nth derivative, depending on how accurate you want the representation to be, and substitute them into the general series given http://en.wikipedia.org/wiki/Taylor_series" .
 
Last edited by a moderator:
sportlover36 said:
how can i find a power series representaion of d/dx (1/x-9)
It looks like you may have some sort of a typo. At x=0, 1/x is infinite.
 
I mean for it to say d/dx (1/(x-9)) sorrry
 
sportlover36 said:
how can i find a power series representaion of d/dx (1/x-9)

This expression can be written as -1/9 * d/dx (1/(1-x/9)). Then think geometric series. Can you see it from there?
 

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