Let $g(x) = e^{-1/x^2}$ for $x$ not equal to zero, and $g(0) = 0$.
a) Please Show that $g^{(n)}(0) = 0$, for all $n = 0,1,2,3,4, \ldots$
Can someone please elaborate on the comments below for this one?
b) Please Show that the Taylor Series for $g$ about 0 agrees with $g$ only at $x = 0$.
I think this would be easy once I have part a, all I have to do is plug in n = 0?
Can someone please show how to do this?