Question

laplace transform of a periodic functions

Answer 1

What is this you're doing lol

Answer 2

i have taken the Laplace transform of some periodic functions

i dont know how to check if i have done it right

Answer 3

i have used

\[\mathcal L\{f(x)\}=\int\limits_0^\infty f(x)e^{-px}\text dx\]
\[=\int\limits_0^\tau f(x)e^{-px}\text dx+\int\limits_\tau^{2\tau} f(x)e^{-px}\text dx+\int\limits_{2\tau}^{3\tau} f(x)e^{-px}\text dx+\dots\]\[=(1+e^{-p\tau}+e^{-2p\tau}+\dots)\int\limits_0^\tau f(z)e^{-pz}\text dz\]\[=\frac{1}{1-e^{-p\tau}}\int\limits_0^\tau f(z)e^{-pz}\text dz\]

Answer 4

how do you type a document like that is it LaTex ,it looks great csry i cant help with the content but the presentation is fine hw do you create such a presentation

Answer 5

i have been using a program called TeXShop

Answer 6

How sure are you that it converges?

Answer 7

i dont know

Answer 8

As long as the function grows slower than Me^pt then it converges.

Answer 9

ok it converges because the slope is only positive or negative 1 , which is less slope than any exponential

Answer 10

Yeah, I'm not sure of the name of the theorem but I just went over that in one of my classes not too long ago.

Answer 11

geometric series?