I am given the sequence of functions $f_n(x)=e^{-nx^2}$ on $[-10,10]$. I must find the pointwise limit function $f(x)$ and decide whether convergence is uniform. If it is, I must find a $B_n$ such that $f_n(x) \leq B_n$ for all $n$ and $B_n \rightarrow 0$. If not, I must find an $\epsilon > 0$ and a sequence $x_n$ such that $|f_n(x_n) - f(x_n)| \geq \epsilon$ for all $n$
I determined the pointwise limit function to be $f(x)=\begin{cases} 1 & x = 0 \newline 0 & otherwise \end{cases}$
However, I am having trouble with the second step. I presume it is not uniformly convergent, since it will have a jump as $x \rightarrow 0$. I do not know what $\epsilon$ to work with here. I tried solving it for $x_n$ but I got something like $f_n(x_n) \leq -\epsilon$ which doesn't seem right.