How Do You Correctly Apply Taylor Series Expansion for f(x-dx)?

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Discussion Overview

The discussion centers on the correct application of Taylor series expansion for the expression f(x-dx). Participants explore the nuances of substituting values into Taylor series and the implications of different expansion points.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the validity of directly substituting x-dx into the Taylor series for f(x), suggesting that this approach is incorrect.
  • Another participant provides a standard form of the Taylor series, indicating that it typically involves an expansion around a specific point, which is often zero (MacLaurin series).
  • A different participant raises the issue of using dx, questioning how it fits into the Taylor series framework and references an external source for a formula that they do not fully understand.
  • Another participant clarifies the terminology around dx, suggesting it represents a change in x rather than a second point, and recommends a resource that explains the Taylor series expansion in detail.
  • One participant emphasizes the importance of specifying the point of expansion when discussing Taylor series, noting that coefficients will differ based on the chosen point.

Areas of Agreement / Disagreement

Participants express differing views on the correct method for applying Taylor series expansion, with no consensus reached on the appropriate approach or terminology.

Contextual Notes

There are unresolved issues regarding the assumptions made about dx and its role in the Taylor series, as well as the dependence on the point of expansion for the coefficients.

saadsarfraz
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Hi, how would you find the taylor series for f(x-dx). i know that substituting x-dx in the series for f(x) is not correct.
 
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You are using an unusual terminology. Typically a Taylor series looks like:

f(a+x)=f(a) + xf'(a) + x2 f''(a)/2! + ...

When a=0, it is called a MacLaurin series.
 
what happens if you have dx instead of a. the second post on this website http://www.wilmott.com/messageview.cfm?catid=19&threadid=17563
has a formula but i don't know how it was derived.
 
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u are using dx in the sense of a second point of x, or a change in x
check out this page from wikiversity that breaks everything down really well.
normally i know that posts from wiki are frowned upon, but i learned from this site and i think they break it down really rigorously and guide you nicely through the expansion of a function into a summed power series and then into taylors series at different points.
http://en.wikiversity.org/wiki/Taylor's_series
 
Saying "Taylor Series" is not enough, you have to attach a point around which you are expanding the function. Notice that around a different point, the taylor series will also have different coefficients.

In your example, f(x+dx) was calculated around a point x, so of course substitution won't work for the exapnasion of f(x) around 0.
 

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