Solution
= Solution
For every fixed $x>0$, $nx^2\to\infty$, so the <pointwise limit> is zero. But $\sup_{0<x<1}e^{-nx^2}=1$ for every $n$, since $x$ can approach zero. Hence \b[convergence is not uniform]. For an explicit moving-point test take $x_n=n^{-1/2}$ for $n>1$, which gives $F_n(x_n)=e^{-1}$.