For each n E N, define a fn : D = (-co, 1] -> R by fn(2) = 1 - - nx \ /2 n +1 n 2 1. 1. Determine, with motivation, lim fn(x) on D. 2. Find, with motivation, the largest set Do C D such that lim fn(x) in Ques- n-+0o tion 1 exists. 3. Prove that the sequence (fn)=1 converges pointwise on Do to the limit func- tion f determined in Question 2 above. 4. Does the sequence (fn) 1 converge uniformly on Do to the limit function f determined in Question 2 above? Justify your