Find the Taylor Series for 28^(3/5) Up to First Order – Tips & Suggestions

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Homework Help Overview

The discussion revolves around finding the Taylor series for the expression 28^(3/5) up to the first order, specifically focusing on the polynomial to use for this approximation.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster inquires about the appropriate polynomial for the Taylor series, suggesting x^3 around 2. Some participants propose using the Taylor series of the function f(x)=x^(3/5) around a=32, while others question the choice of the point of expansion.

Discussion Status

The conversation is ongoing, with participants exploring different points of expansion and clarifying the reasoning behind their suggestions. There is no explicit consensus yet, but various interpretations are being discussed.

Contextual Notes

Participants are considering the proximity of 32 to 28 in the context of Taylor series expansion, which may influence the choice of expansion point.

peripatein
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Hello,

What polynomial should I use for finding Taylor series for 28^(3/5) up to the first order? I mean, aside x^3 around 2. Any suggestions?
 
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Use the Taylor series of f(x)=x^(3/5) around a=32 (=2^5).

ehild
 
Did you not mean to write =2^3 (Instead of "=2^5")?
 
I know that 32=2^5.
 
Yes, and that is the fifth power of an integer that is closest to 28. That's the point.
 

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