Let g_h (x) = \begin{cases} e^{-\frac{1}{(x^2 - h^2)^2}, & |x| < h,\\ 0, & |x|\ge h. \end{cases} = \begin{cases} \exp(-(x^2-h^2)^{-2}), & |x| < h,\\ 0, & |x|\ge h\end{cases}.

||g_h^{(n)}|| = \max_{|x|<h} |g_h^{(n)}(x)|, where g_h^{(n)} is the nth derivative of g_h.

Prove that \lim_{h\to 0} ||g_h^{(n)}|| = 0