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Easy limit problem

  1. Feb 25, 2008 #1

    tony873004

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    [tex]\mathop {\lim }\limits_{t \to 1} \,\frac{{t - 1}}{{t^2 - 1}}[/tex]

    I thought we were taught to simply divide the coefficients of the highest term, in this case, 0t2 for the numerator and 1 t2 for the denominator. 0/1=0. But I know the limit is 0.5 from substituting 0.9999999999 for t in my calculator.

    I must be getting this "coefficient of highest term" method mixed up with something else. Why doesn't it work here?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 25, 2008 #2
    well what u need to do is
    [tex]t^{2}-1=(t-1)(t+1)[/tex]
    can u go from here?
    This is just the difference of squares. Its general form is:

    [tex]a^{2}-b^{2}=(a-b)(a+b)[/tex]
     
    Last edited: Feb 25, 2008
  4. Feb 25, 2008 #3

    HallsofIvy

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    I strongly suspect you were taught that for limits as t goes to infinity! That is not the problem here.

     
  5. Feb 26, 2008 #4

    tony873004

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    Thanks for the explanation, sutupid.

    You're probably right, Halls. I'll never forget this now. This was part of a larger problem in Calc III. That's the problem with Calc III. Every now and then they assume you remember your Calc I :)
     
  6. Feb 26, 2008 #5
    Honestly, this had almost nothing to do with calc I, it was just a simple algebra trick!
     
  7. Feb 26, 2008 #6

    HallsofIvy

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    Well, the tiny part about finding the limit might be from calculus I!
    (And you did say "almost nothing".)
     
  8. Feb 26, 2008 #7

    tony873004

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    Algebra class was 20 years ago for me. Everything I currently know about Algebra I learned in Calc I.
     
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