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Quick Question On Limits

  1. Feb 20, 2007 #1
    I was wondering if Limits commute,

    Ie:
    Limit of z to infinity[ Limit of z to 0[ f(0)/z ]]

    =

    Limit of z to 0[ Limit of z to infinity[ f(0)/z ]]

    Edit: Nvm, they dont... I just did a some test functions... I'm just hoping for an easy way to finish one of my proofs.

    Though on a sidenote, integrals and limits do commute right?
     
    Last edited: Feb 20, 2007
  2. jcsd
  3. Feb 20, 2007 #2

    AKG

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    This doesn't even make sense. The only way "Limit of z to A[Expression]" even makes sense is if z is a free variable in the Expression. But in both "Limit of z to 0[ f(0)/z ]" and "Limit of z to infinity[ f(0)/z ]", z is NOT a free variable. Note that in "f(0)/z", z is a free variable, but in "Limit of z to B[ f(0)/z ]", it is not. (In the above, A and B can of course be anything, not just 0 and infinity which you've used in your examples). So I don't see how you could have determined:

    Edit: Nvm, they dont... I just did a some test functions...

    since it doesn't even make sense.

    And integrals and limits don't always commute.
     
    Last edited: Feb 20, 2007
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