Continuity of $e^{-1/x^2}$

Asked Jan 20 '14 at 00:25

Active Jan 20 '14 at 00:43

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Let $$f(x)=\begin{cases}e^{-1/{x^2}} & x\neq0\\ 0 & x=0\end{cases}$$

Show $f(x)$ is continuous
Show that the $n$-th derivative is continuous.

I've seen this a couple of ways but I'm struggling with an epsilon delta proof of the the first part. I know (in theory) how to get the second part once I have that.

edited Jan 20 '14 at 00:43

user127.0.0.1

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asked Jan 20 '14 at 00:25

BFuchs

1

You may want to check this out: http://math.stackexchange.com/questions/119858/infinitely-differentiable-function. Cheers! – Dmoreno Jan 20 '14 at 00:29
Yea I get that part. My problem is first doing the epsilon delta proof of the first part. – BFuchs Jan 20 '14 at 00:32
Let $\delta = \frac{1}{\sqrt{\ln(1/\epsilon)}}$ – IAmNoOne Jan 20 '14 at 00:46

Continuity of $e^{-1/x^2}$

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