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...

agree?

 

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.