I have some trouble wrapping my head around singularity(adsbygoogle = window.adsbygoogle || []).push({});

One of assignment question is to show that the unit function is not defined at 0. To do that, I need to show

[tex]\lim_{\Delta\to0}[u_{\Delta}(t)\delta(t)]=0[/tex]

[tex]\lim_{\Delta\to0}[u_{\Delta}(t)\delta_{\Delta}(t)]=\frac{1}{2}\delta(t)[/tex]

Also, I need to show that the following is identical to u(t)

[tex]g(t)=\int u(t)\delta(t-\tau)d\tau[/tex]

integrating from negative infinity to positive infinity

One more question, what's the derivative of the impulse function?

PS: what's the tex code for integration from infinity to infinity? I tried \int_-\infty^+\infty, but the tex output is messed up

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# Need help with Impulse function and unit step function at singularity

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