Verify that the sequence of functions (left{f_{n}(x) ight}_{n=1}^{infty}), defined by (f_{n}(x)=) (frac{n}{2} e^{-n|x|}), approaches a delta function.

Verify that the sequence of functions \(\left\{f_{n}(x)\right\}_{n=1}^{\infty}\), defined by \(f_{n}(x)=\) \(\frac{n}{2} e^{-n|x|}\), approaches a delta function.