The function is (s-10)/((s^2 +20s)). I am trying to understand how to compute the final and initial value of the function with a unit step impulse. If I take the lim @ inf, using l'hopital's rule I get 0 this should be the final value. However, if I take the lim @ 0 I also get 0 and this should be my initial value. So I am confused. Does l'hopital's rule not apply to this function? I do get an indeterminate form of inf/inf.

If I put the function into wolfram I get an output plot that looks like what I would expect from 1/(s+a) if I were to check the limits at inf and 0 with a unit step input. However, if I create the transfer function in matlab and apply the unit step I get an output that looks like 1/(s+a) had I applied a ramp function to it.

Can someone tell me why taking the limit of this function at inf leads to 0 when it should lead to -inf according to matlab with a unit step input but according to wolfram it leads to 0. Is the output that matlab gave me just the time domain output that wolfram gave me but multiplied by 1/s and why doesn't take the lim @ 0 give me the value .2 which is the amplitude of the impulse displayed on the wolfram output. For instance, lim @ 0 of 1/(s+a) = 1/a which would be the final value but also the amplitude of the initial impulse given that my input is a step.

Please help. I am obviously confused.