I'm not too sure how to do this, so any help would be great:

fn(x) = n/(1+nx^2) on (0, infinity)

a) find the pointwise limit

b)prove (or disprove) if the sequence converges uniformly.

I don't really know how to find the pointwise limit because I can't factor the denominator, and I can't separate the numerator into two fractions (like the examples in the book).

Also, I have another one that is a bit different:

fn(x) = sin(nx)/1+nx on [1,2].

How do I figure out the pointwise limit on that domain?