Hey, I'm pretty sure I already solved part a. of this question, but decided to put it up just in case. Any help would be greatly appreciated. Thanks.

Let fn(x) = nx / (1 + nx^2)

a. Find the pointwise limit of (fn) for all x Є (0, infinity).

b. Is the convergence uniform on (0, infinity)?

c. Is the convergence uniform on (0,1)?

d. Is the convergence uniform on (1, infinity)?