Question

. Show that f: \mathbb{R} \longrightarrow \mathbb{R}, \quad x \mapsto\left\{\begin{array}{l}

e^{-\frac{1}{|x|}} \quad x \neq 0 \\

0 \quad x=0

\end{array}\right. \text { is } C^{\infty} \text { function. Calculate the } n \text {-th derivation } \frac{d^{n} f}{d x^{n}}(0) \text { for arbitrary } n \in \mathbb{N} \text {. }

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