1. The problem statement, all variables and given/known data http://gyazo.com/55eaace8994d246974ef750ebeb36069 2. Relevant equations Theorem III : http://gyazo.com/af2dfeb33d3382430d39f275268c15b1 3. The attempt at a solution At first this question had me jumping to a wrong conclusion. Upon closer inspection I see the sequence converges to 1 as n goes to infinity for |x|<1. The sequence converges to 0 as n goes to infinity for |x|≥1. Hence the sequence is not uniformly convergent over the whole real line. If we restrict the domain of x to (-1,1) or (-∞,-1] U [1,∞), then we can observe uniform convergence over each interval respectively. The question isn't too clear about what it's asking for, but that's my take.