# Limit of u(t)- u(t -\delta) as delta goes to zero, LTI systems

1. Feb 7, 2010

### AMac33

1. The problem statement, all variables and given/known data

what is the limit of yb(t) as \delta goes to zero.

yb(t) = (b/delta)*exp[-t/RC](exp[delta/RC] - 1)(u(t)-u(t-delta))

b=1.

2. The attempt at a solution

I used L'hopitals rule to find the limit of (b/delta)*exp[-t/RC](exp[delta/RC] - 1), which i got to be exp[-t/RC]/RC.

But I do not know what to do with the u(t)-u(t-delta). does it go to zero? or am I supposed to say it goes to delta(t)?

Any help/ advice would be appreciated, thanks!

2. Feb 7, 2010

### CompuChip

Does the expression

$$\lim_{\delta \to 0} \frac{u(t + \delta) - u(t)}{\delta}$$
ring a bell?

3. Feb 7, 2010

### AMac33

honestly, no. I'm fairly new to the unit step and dirac delta function.

4. Feb 7, 2010

### CompuChip

Oh, but this doesn't have to do with either of those. $\delta$ is just a variable, if it makes you feel any better you can call it x or (more commonly used) h

Maybe I should ask it the other way around: what is the definition of the derivative u'(t) of u(t) at t?