I just dont know where to start!

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Discussion Overview

The discussion revolves around a homework problem involving the calculation of the Maclaurin series for a specific function, which is defined piecewise. Participants are exploring the concept of non-analytic functions and the convergence of series.

Discussion Character

  • Homework-related
  • Exploratory
  • Technical explanation

Main Points Raised

  • The original poster expresses confusion about starting the problem involving the function f(x) = e^(-1/x^2) for x ≠ 0 and f(0) = 0, and seeks assistance.
  • One participant questions the notation used for "e" in the function, suggesting it should be e^x.
  • The original poster clarifies that it is indeed e^x and continues to express difficulty in understanding the problem.
  • Another participant provides links to resources summarizing the Maclaurin series and Taylor series, indicating these might be useful for the original poster.
  • A later reply suggests considering the purpose of series expansion and the criteria for convergence, hinting at the broader context of the problem.

Areas of Agreement / Disagreement

Participants generally agree on the need to understand the Maclaurin series and its application to the given function, but there is no consensus on how to approach the problem or on the specifics of the function's notation.

Contextual Notes

The discussion highlights a lack of clarity regarding the function's notation and the steps needed to calculate the Maclaurin series, as well as the concept of convergence, which remains unresolved.

Who May Find This Useful

Students studying calculus, particularly those interested in series expansions and the properties of analytic versus non-analytic functions.

rcmbimp
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Non analytic function?

Homework Statement



I was set this question as part of an extra problem sheet by my maths teacher, and i don't know where to start. He said its like first year university maths standard, and gave me hints to use the maclaurins and binomial series. I am just a bit stuck... PLEASE HELP... I found an example of a non analytical function on this forum, but just confused me!

the question...

Consider the function
f(x) = "e− 1
x2 if x "= 0
0 if x = 0
.
Calculate the Maclaurin series of f and show that it does not converge to f(x) for x "= 0. In
particular f is not an analytic function.

Homework Equations



Maclaurins series
Binomial expansion

The Attempt at a Solution



I don't know where to start
 
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woops... can't copy and paste!

Yes sorry it is an e^x...

Thanks for yuor reply, but I am still really stuck. I emailed my teacher the other day and he said to try find an example, and just understand it (or try to understand it).

Does anyone know where i could find a worked solution of this... preferablely with quotations as it goes along...

thanks
rcmbimp
 
rcmbimp said:
Yes sorry it is an e^x...

Thanks for yuor reply, but I am still really stuck. I emailed my teacher the other day and he said to try find an example, and just understand it (or try to understand it).

Does anyone know where i could find a worked solution of this... preferablely with quotations as it goes along...

This page has some good examples regarding convergence of a series.
http://www.math.ubc.ca/~indurskis/math100/taylor/example6.html

Think about the purpose of expanding using a series and then think about the criterion for convergence.
 
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