Simple check (book wrong)

Discussion in 'Homework Help' started by ihaveaquestion, Nov 4, 2009.

  1. ihaveaquestion

    Thread Starter Active Member

    May 1, 2009
    I'm pretty sure the book is wrong on this:

    Asked to find the initial and final values of

    G(s) = 3s^3+2s+10 / s(s+2)^2(s+3)

    initial-value theorem says that f(0)= lim(s->infinity) of sF(s) which comes out to 3 and I agree with that

    however for the final-value theorem I disagree....

    the book says its 0.833 but I believe it's 0.

    final-value theorem says f(infinity)=lim(s->0) of sF(s)

    If you divide 10/(2^2+3) thats 0.833, but that means you didnt multiply the numerator by s in the case... in other words:

    sG(s) = 3s^4+2s^2+10s / s(s+2)^2(s+3)

    You can see that as you take the limit of s approaching 0, the numerator will become 0 and the whole thing is 0...

  2. StayatHomeElectronics

    AAC Fanatic!

    Sep 25, 2008
    f(infinity)=lim(s->0) of sF(s)

    G(s) = 3s^3+2s+10 / s(s+2)^2(s+3)

    sG(s) = s (3s^3+2s+10) / s (s+2)^2(s+3)
    sG(s) = (3s^3+2s+10) / (s+2)^2(s+3)

    you can simplify since both numerator and denominator have an s.

    If you do not simplify you would get 0 in both the numerator and denominator.