### Sequences : Limits and Convergence

This question is from Advanced Calculus II class, it is more like introduction to real analysis. Let f_n: R -> R be the sequence of functions given by f_n(x) = x/ ( 1 + nx^2) a). Prove that the sequence f_n converges uniformly to a function f. What is f? b). Prove that for each x in R-{0} ( all real numbers but 0 not in