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How does this second integral equal +infinity instead of -infinity?

  1. May 5, 2013 #1
    1. ...How does this 2nd integral diverge to +∞? It seems to me that it would diverge to -∞... :/

    lim ([itex]\frac{-1}{a - 1}[/itex] - [itex]\frac{-1}{0 - 1}[/itex]) + lim ([itex]\frac{-1}{2 - 1}[/itex] - [itex]\frac{-1}{b - 1}[/itex]) + lim ([itex]\frac{-1}{c - 1}[/itex] - [itex]\frac{-1}{2 - 1}[/itex])
    a→1- b→1+ c→∞

    2. First integral: -1/(tiny negative #) - 1 = +∞

    Second integral: -1 + 1/(tiny negative #) = -1 + -∞ = -∞ <----This answer is supposed to be +∞. How?!

    Third Integral: -1/(∞ - 1) + 1 = 0 + 1 = 0

    The only thing I don't get it the second integral! :(
    Help please!
    Thanks! :)
     
    Last edited: May 5, 2013
  2. jcsd
  3. May 5, 2013 #2

    HallsofIvy

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    It is NOT "tiny negative". [itex]-\frac{-1}{b- 1}= \frac{1}{b- 1}[/itex] and b is approaching 1 from above so b> 1 and b- 1> 0.

     
  4. May 5, 2013 #3
    If b is approaching 1 from the right, it seems like it would be very close to the number 1.

    Maybe it would be 1.00000000001

    So 1/(1.00000000001 + 1) = 1/.00000000001 = +∞

    I usually pay no attention to the - or + in the limit, but I see it's important! O_O
    Thanks!
     
  5. May 5, 2013 #4

    SteamKing

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    These are not integrals: they are limits.
     
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