Taylor Expansion of f+df About x?

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Discussion Overview

The discussion revolves around the Taylor expansion of the expression f + df about a variable x. Participants explore the meaning of the terms involved and the appropriate context for performing the expansion, addressing potential misunderstandings and definitions required for clarity.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions the meaning of f + df and its relationship to x, suggesting that context is necessary for a proper answer.
  • Another participant asserts that f is a function of x and possibly other variables, implying that the expansion should consider these dependencies.
  • A participant emphasizes that Taylor expansions should be performed around a fixed base point, indicating that expanding around a variable is not appropriate.
  • There is a contention about the necessity of defining variables, with one participant arguing that without definitions, the question becomes meaningless.
  • A later reply provides a formulation of the Taylor expansion, indicating a resolution for the original poster but also reflecting on the earlier debate about definitions.

Areas of Agreement / Disagreement

Participants express disagreement regarding the necessity of defining terms and the proper approach to the Taylor expansion. The discussion does not reach a consensus on these points, as some participants emphasize the importance of context while others focus on the mathematical procedure itself.

Contextual Notes

The discussion highlights limitations in the initial question due to undefined terms and the ambiguity surrounding the variables involved. The lack of clarity in the definitions of f and df contributes to the confusion about the expansion process.

rexregisanimi
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How would one expand f+df about x? I'm messing something up in the process and can't seem to resolve it lol
 
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What does f+df mean?
How are they related to x?

There is way too much context missing to answer that.
 
It shouldn't matter; f is a function of x (and other variables)...
 
rexregisanimi said:
It shouldn't matter; f is a function of x (and other variables)...

You can't Taylor expand around a variable. You expand around a fixed base point. That's why we write the polynomials terms as ##(x-a)^n##, i.e. expand around a.
 
rexregisanimi said:
It shouldn't matter;
It does matter. Letters without any definition are pointless.
It is like asking "what is x+y?" You cannot answer it (apart from "it is x+y") if you have no idea what x and y are.
 
Wow...

I was either communicating poorly or something. I found my answer.

f+df = f +(df/dx)dx + (d2f/dx2)dx2 + ... [The parenthetical terms are partials but not the differentials.]

My favorite is, "It does matter. Letters without any definition are pointless." And to think I wasted all that time learning Algebra! :/
 

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