Define the function $h(x)$ by setting $h(x) = e^{-1/x^2}$ if $x>0$ and $0$ if $x \leq 0$. 

1. My question is how can I show $h(x)$ is in $C^{\infty}$?
2. Let $\| \mathbf{x} \| = \max\_{i=1,2} | x\_i |$. Then is 
$h(\| \cdot\|) : \mathbb{R}^2 \rightarrow \mathbb{R}$ in $C^{\infty}$ as well?