Define f:R->R by fx = 0 if x<=0 and e^-1/x if x>0(adsbygoogle = window.adsbygoogle || []).push({});

Show that f is c^inf and that all the derivatives of f at 0 vanish; that is, f^(k)0=0 for every k.

After taking first and secondderivatives we just apply l'hostpials rule to show that the derivatives vanish.

My problem is for the kth derivative.

We know after taking the derivative we get some polynomail say p(x) so

f^k(x) = p(x) * e^-1/x

What do I do now?

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# Homework Help: Manifolds 2

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