Prove the uniform convergence of the sequence of real valued function

Question

$$f_n=xe^{-nx^2}, x\in R, n\in N.$$ Prove that the sequence {${f_n}$} is uniformly convergent in $R$. Some good arguments to prove this please?

Answer 1

HINT It converges pointwise to $0$. Now recall the definition of uniform convergence and find the supremum of $f_n(x)$ by maximizing it (you should get $e^{-1/2}/\sqrt{2n}$).