Let fn(x) = x^n/(1 + x^n ), and A = [0, ∞) Use the ∆n-metric criterion to show that (fn) does not converge uniformly on

[answerhappygod]

Let fn(x) = x^n/(1 + x^n ), and A = [0, ∞)
Use the ∆n-metric criterion to show that (fn) does not converge
uniformly on [0, 1] 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) does not converge to 0, then by the squeeze theorem (∆n)
does not converge to 0.