Let fn(x) = sin(nx)/(1 + nx), and A = [0, ∞) Let a > 0. Use the ∆n-metric criterion to show that (fn) converges uniforml

[answerhappygod]

Let fn(x) = sin(nx)/(1 + nx), and A = [0, ∞)
Let a > 0. Use the ∆n-metric criterion to show that (fn)
converges uniformly on [a, ∞) to f∗;
Some helpful information to do the problem:
1.) ∆n = sup{d(fn(x),f*(x)}
2.) (fn) converges to f* uniformly on A iff (∆n) converges to 0
as n goes to infinity
3.) If there exists a ∆'n such that ∆'n >= ∆n,
for all n and (∆'n) converges to 0, then by the squeeze theorem
(∆n) converges to 0.