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Let $f$ be defined on $\mathbb{R}$ by $f(x) = e^{-1/x^2}$ for $x$ not equal to $0$. and $f(0)= 0$. Prove that $f^{(n)}(0)=0$ for all $n = 1, 2,3$ ...

Do I need to use Taylor expansion from calculus class?

Any hint would be appreciated.

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    Calculate a few derivatives of the function and look for common features.2012-12-13
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    So after finding common features? Can I prove this using induction?2012-12-13
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    Well, what common features did you find?2012-12-13

3 Answers 3