Thread: Laplace transform of delta(t - a)

Hi all,

I am trying to determine the laplace transform of dirac delta function,
delta(t - a).

I end up with:

lim as k ---> 0 [e^(-as) -e^(-as)*e^(-sk)]/ (s*k)

I then use L'Hopitals rule... but i can't seem to get

lim as k--> [s*e^(-as)*e^(-sk)]/ s

Could someone please show me how to get the above equation using L'Hopitals rule... some reason i get 2 other terms which i can't seem to cancel.

Thanks in advance,
ArTiCK

Originally Posted by ArTiCK

Hi all,

I am trying to determine the laplace transform of dirac delta function,
delta(t - a).

I end up with:

lim as k ---> 0 [e^(-as) -e^(-as)*e^(-sk)]/ (s*k)

I then use L'Hopitals rule... but i can't seem to get

lim as k--> [s*e^(-as)*e^(-sk)]/ s

Could someone please show me how to get the above equation using L'Hopitals rule... some reason i get 2 other terms which i can't seem to cancel.

Thanks in advance,
ArTiCK

Substitute into the definition for Laplace Transform and then use the sifting property of the Dirac Delta function.