I just dont know where to start!

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The discussion revolves around a math problem involving the function f(x) defined as e^(-1/x^2) for x ≠ 0 and 0 for x = 0. The user is struggling to calculate the Maclaurin series for this function and understand why it does not converge to f(x) for x ≠ 0, indicating that f is not an analytic function. There is confusion regarding the notation and the concept of non-analytic functions, with the user seeking examples and worked solutions for better understanding. Participants suggest focusing on the criteria for convergence and provide links to resources about series expansion. The conversation highlights the challenges of grasping advanced mathematical concepts and the need for clear examples.
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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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