I have to prove that Dirac delta function $\delta$ is equal to this limit:
$$ \delta(x) = \lim_{a\to \infty}\frac{sin(ax)}{\pi x}.$$
We can say, show that the result of the right side of equality is defined as Dirac function:
$$ \delta(x) = \begin{cases} +\infty, & x=0, \\ 0, & x\neq0. \end{cases} $$
Thank you for help.