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?