I just dont know where to start!

[rcmbimp]

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

 

[Astronuc]

f(x) = "e− 1

What is "e?

e^x would make sense.

Here is a summary of the Maclaurin series, which is just the Taylor series expanded about x = 0.
http://mathworld.wolfram.com/MaclaurinSeries.html

http://mathworld.wolfram.com/TaylorSeries.html

See also this
http://en.wikipedia.org/wiki/Taylor_series#List_of_Taylor_series_of_some_common_functions

 

[rcmbimp]

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

 

[Astronuc]

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.