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Limits and Integrals

  1. Feb 28, 2007 #1
    If you are taking the limit of an integral, can you switch the composition ie: take the integral of a limit if the limit and integral are on seperate variables?

    Ie:

    Lim of z to a [integral over alpha [f(x)/((x-z)(x-a)^2) dx]

    =

    Integral over alpha[Lim of z to a[f(x)/((x-z)(x-a)^2) dx]

    =

    Integral over alpha[f(x)/(x-a)^3 dx]
     
  2. jcsd
  3. Feb 28, 2007 #2

    dextercioby

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    Science Advisor
    Homework Helper

    Since an integration involves limits, and switching the order of taking limits is a tricky business, i'd say that you could do the permutation, as long as there's no infinity (or no indeterminate expression under the limit sign) involved...My guess...
     
  4. Feb 28, 2007 #3

    HallsofIvy

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    Science Advisor

    Generally speaking, if both limit and integral are "uniformly convergent" then they can be interchanged.
     
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