#### silveredition

##### Newbie level 6

1) g(x) non-negative on [0 2], and continuous

show that if the mean of g(x) = 0 over this interval, then g(x) must = 0

2) Let { fn } be a sequence of functions with the following property:

fn converges

for each fn(x), lim of fn(x) as |x|->infinity = 0

If f(x) = lim of fn(x) as n->infinity (the convergence of the sequence), then prove that

lim of f(x) as |x|->infinity = 0 as well.

Any ideas?