Can someone help me prove the following:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]L=\mathop \lim\limits_{k\to \infty}\int_{-\frac{3}{4k}}^{\frac{3}{4k}} f(x)[-\frac{16k^3}{9}x^2+k]dx=f(0)[/tex]

I'm pretty sure at the limit,

[tex]-\frac{16k^3}{9}x^2+k[/tex]

becomes a delta function.

Essentially, it's that section of a narow parabola above the x-axis growing taller and more narrow with increasing k. The limits are it's roots and the area is always 1 between the roots.

I can prove the case for the simple square-wave pulse version of delta using the intermediate value theorem for definite integrals but I don't know how to approach the above one. I'd like to show more work but I don't have anymore. It's a hard limit to evaluate for me.

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# A parabola delta function

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