Non analytic function?

1. Dec 26, 2006

rcmbimp

Non analytic function???

1. The problem statement, all variables and given/known data

I was set this question as part of an extra problem sheet by my maths teacher, and i dont know where to start. He said its like first year university maths standard, and gave me hints to use the maclaurins and binomial series. Im 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.

2. Relevant equations

Maclaurins series
Binomial expansion

3. The attempt at a solution

I dont know where to start

2. Dec 26, 2006

Astronuc

Staff Emeritus
3. Dec 28, 2006

rcmbimp

woops... cant copy and paste!

Yes sorry it is an e^x....

Thanks for yuor reply, but im 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

4. Jan 11, 2007

Astronuc

Staff Emeritus