In this problem you will show that the sequence of functions [f_{n}(x)=frac{n}{pi}left(frac{1}{1+n^{2} x^{2}} ight)] approaches (delta(x)) as (n ightarrow infty). Use the following to

In this problem you will show that the sequence of functions

\[f_{n}(x)=\frac{n}{\pi}\left(\frac{1}{1+n^{2} x^{2}}\right)\]

approaches \(\delta(x)\) as \(n \rightarrow \infty\). Use the following to support your argument:

a. Show that \(\lim _{n \rightarrow \infty} f_{n}(x)=0\) for \(x eq 0\).

b. Show that the area under each function is one.