Using Taylor Polynomial for Laplace Transforms

[jofree87]

Ive attached the problem and my work in the pic.

Questions:

Am I even applying the taylor polynomial the correct way? (I never learned taylor series, but I was supposed to be taught in the pre-requisite class)

Am I suppose to plug in c=4? I am not so sure about how the U₄(t) works.

After I have found the taylor polynomial, do I just take the laplace transform of it, and then that is my answer?

thanks

 

[LCKurtz]

In this problem you want to make use of the forumula

\mathcal L(f(t-a)u(t-a) = e^{-as}\mathcal Lf(t)

but you need to take the transform of f(t)u₄(t) = f(t)u(t-4), which isn't in that form. So to use the above formula, you need to express f(t) in powers of (t-4).

Once you have the Taylor polynomial, you would take its transform as though all the t-a terms were t and multiply the result by e^-as.

I didn't check your arithmetic but be sure you go up through the 4th derivative since you have a 4th degree polynomial and the 5th derivative and above would be 0.

[Edit] Your numbers are OK but you need that last term to get the 4th degree.

 

[jofree87]

ok, I see now. Thanks for the help!