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What is the limit of

  1. Oct 4, 2005 #1
    what is the limit of ......

    I am a physics student. While I was doing problem concerned with moment of inertia, I got stuck at a point. I got the moment of inertia of a material line as


    lim a -> 0 (3ab)/(a^3 + b^3)

    What is the limit?
    Thanks in advance for your help
     
  2. jcsd
  3. Oct 4, 2005 #2

    James R

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    The limit for the expression you've written is zero, provided b does not equal zero.
     
  4. Oct 5, 2005 #3

    HallsofIvy

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    And if b= 0, 3ab/(a^3+b^3)= 0 for all a so the limit is still 0!
     
  5. Oct 6, 2005 #4
    Sorry, question was wrong

    I am sorry that the question I posed was not what I supposed. I meant


    lim a->0 (a^3 + b^3)/(3ab)

    Thanks in advance for your help
     
  6. Oct 6, 2005 #5

    ranger

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    It looks like the lim = 0, since a = 0.

    Man its been a while since i did this stuff.
     
  7. Oct 6, 2005 #6

    VietDao29

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    Nope. The limit does not exist here.
    Since b is in the denominator, so [itex]b \neq 0[/itex]
    So
    [tex]\lim_{a \rightarrow 0} \frac{a ^ 3 + b ^ 3}{3ab}[/tex]
    The numerator will tend to b3, while the denominator will tend to 0. So the limit does not exist.
    Viet Dao,
     
  8. Oct 6, 2005 #7

    ranger

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    Does that mean there is an asymptote there or something?
     
  9. Oct 6, 2005 #8

    VietDao29

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    Yup, there's a vertical asymptote there.
     
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