Is the sequence $f_n(x) =xe^{-nx^2}$ uniformly convergent

43 Views Asked by At

Question : Is the sequence $f_n(x) =xe^{-nx^2}$, $n\geq1$,$\forall x > \in \mathbb R$ uniformly convergent in $\mathbb R$

My attempt: $f_n(x) =xe^{-nx^2}$ is convergent pointwise to $f(x)=0$. But I don't know how to prove or disprove uniform convergence.

I am new to uniform convergence and not really good at solving these kinds of problems. Any help would be appreciated.