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

  1. Feb 7, 2010 #1
    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. jcsd
  3. Feb 7, 2010 #2

    CompuChip

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    Does the expression

    [tex]\lim_{\delta \to 0} \frac{u(t + \delta) - u(t)}{\delta}[/tex]
    ring a bell?
     
  4. Feb 7, 2010 #3
    honestly, no. I'm fairly new to the unit step and dirac delta function.
     
  5. Feb 7, 2010 #4

    CompuChip

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    Oh, but this doesn't have to do with either of those. [itex]\delta[/itex] 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?
     
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