### Uniform convergence of sequences of functions

1. Show that the sequence x^2 (e^-nx) converges uniformly on [0, infinity). 2. Show that if a is greater than zero then the sequence (n^2 x^2 (e^-nx)) converges uniformly on the interval [a, infinity) but does not converge uniformly on the interval [0, infinity). For problem 2 text gives a hint that if n is sufficiently larg