- #1
ARozanski
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Homework Statement
[tex] f(x)=\left\{\begin{array}{cc}e^{-x^{-2}},& \mbox{ if } x!=0 \\ 0, \mbox{ if } x=0 \end{array}\right [/tex]
Prove the smoothness of f(x) - as in - prove it has infinite derivatives.
I was asked this question in a calculas class i have in university...It just so happens to be that this question was asked on this site last year =>
LINK: https://www.physicsforums.com/showthread.php?t=135116
The Attempt at a Solution
Now - looking at what the person said last year - they got to what i also got to - which was that after a few derivatives you get - [tex]\frac{c}{x^n}[/tex] where is c is some number
I did not however understand why they had to get to the point where they wanted to multiply the limit of the derivatives with the actual function f(x).
Please can someone point me in the right direction into solving this...i need it done by sunday - any help well be greatly appreciated