I'm having trouble with this problem - I don't even know how to begin. Thoughts? Solutions with explanation? Please help!
Let $f$ be a bounded continuous function on $\mathbb{R}$. Prove that
$$ \lim_{n \to \infty} \frac{n}{\pi} \int_{\mathbb{R}} \frac{f(t)}{1+n^2t^2}dt = f(0).$$