a) For each n $\displaystyle \in$ N consider $\displaystyle F_{n}$ : $\displaystyle [0, \infty) \rightarrow $ R be given by $\displaystyle F_{n}(x) := (x^n)e^{-nx}$. Show that {$\displaystyle F_{n}$}$\displaystyle _{n \in N}$ converges in a pointwise fashion to the zero function on $\displaystyle [0, \infty)$.

b) Decide whether the convergence in part a is uniform on $\displaystyle [0, \infty)$.

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