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Homework Help: Taking the limit of this as s-> 0 (algebra based)

  1. Nov 29, 2008 #1
    1. The problem statement, all variables and given/known data

    Hi all, this may sound trivial but I've been like cranking my brains on this. Probably I just cant see it. Will need someone to shed some light.

    Taking the limit of [(1/s)(a-b)/(s^2 + cs + a)] as s-> 0


    2. Relevant equations

    Stated above

    3. The attempt at a solution

    By using L'Hopital rule, I know this limit tends to 0 itself. However, I just cant manipulate the expression algebraically to obtain the same limit of 0. I'm just unable to cancel out that 'solo' s at the denominator. Hence, it appears to me that the limit shoots up to infinity as s-> 0 through algebraic means. I know this is incorrect but I just couldnt figure it out.

    Please kindly help me in guiding me along.

    Thanks!
     
  2. jcsd
  3. Nov 29, 2008 #2
    You can't use l'Hopital's rule here, because the fraction is not of the form "0/0" or "inf/inf". I understadn what you wrote as
    [tex]
    \lim_{s\to 0}\frac{\frac{1}{s}(a-b)}{s^2+cs+a}
    [/tex]
    The numerator tends to infinity, the denominator however tends to a, so yes, the expression "blows up" as s-->0.
     
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