For each of the following sequences (fn), find the function f such that fn --> f. Also state whether the convergence is uniform or not and give a reason for your answer.
a.) fn(x) = 1/xn for x greater than or equal to 1
b.) fn(x) = x/(1+xn) for x element of [0,1]
The Attempt at a Solution
a. I think the limit function is 1 if x=1 and 0 if x?1. I also think it does not converge uniformly but do not know why.
b. I think the limit function is 0 if x=0 and 1/2 if x=1. I think it does not converge uniformly.