Finding Taylor Series of Functions - Tips to Make it Easier

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Homework Help Overview

The discussion revolves around finding the Taylor series of the function f(x) = ln(x) about the point x = e. Participants express challenges in navigating the process of deriving the series, particularly in the context of calculus coursework.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the importance of ensuring the function is analytic at the point of expansion and suggest differentiating the function to derive the series. There are mentions of gathering information about the function's values and derivatives at the point of interest to identify a pattern.

Discussion Status

The conversation includes various suggestions on how to approach the problem, with some participants offering general advice on differentiation and series formation. There appears to be a lack of consensus on specific steps, but guidance on the analytical nature of the function and the need for derivatives has been provided.

Contextual Notes

Participants note that this topic is particularly challenging within the broader scope of Calculus II, indicating a potential struggle with the material.

pnazari
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I was wondering if someone can give me some tips for finding the taylor series of functions. For example this was a test question we had:

Find the taylor series of f(x)=ln(x) about x=e

I know how to start it off but I get confused halfway through and can't seem to figure out what to do. Are there some simple steps? Any help/tips will be appreciated.

For me, this is the hardest section of Calc. II
 
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There aren't really any advice here.You just make sure the function is analytical in that point,which,in this case is...

So differentiate and write that series...

Daniel.
 
Find as much information as you can about f(x), usually f(e), f'(e) f''(e) if u can get that far. then find a pattern from there and write a series.
 
Thankfully,the power function can easily differentiated any # of times,so this problem is really simple.


Daniel.
 

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