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Homework Statement
$$ y(s) = \frac {s}{(s+1)(2s+1)} u(s) $$
Where ##u(s)## is the step function ##\frac {1}{s}##
Find the output at t=0 and t= infinity
Homework Equations
The Attempt at a Solution
My question is kind of basic, so I know the final and initial value theorem
$$ \lim_{s \to 0} sY(s) = \lim_{t \to \infty} y(t) $$
But should I include the step function, or leave it out. Meaning, should I evaluate
$$ \lim_{s \to 0} \frac {s^{2}}{(s+1)(2s+1)} \frac {1}{s}$$
or rather,
$$ \lim_{s \to 0} \frac {s^{2}}{(s+1)(2s+1)} $$
The reason I am hesitating on this is because in the textbook example problem, they do not mention what the input function is, and proceed to solve without the step function. Then I solved a homework problem where they asked to match the transfer function output with a step function input, and at that time I did not even realize, so I was only doing limits of Y(s), not sY(s), and got them all right. So now my head is all jumbled up and I just want to get this thing cleared up!