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Limits and Integrals 
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#1
Feb2807, 02:50 AM

P: 207

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)/((xz)(xa)^2) dx] = Integral over alpha[Lim of z to a[f(x)/((xz)(xa)^2) dx] = Integral over alpha[f(x)/(xa)^3 dx] 


#2
Feb2807, 03:19 AM

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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...



#3
Feb2807, 11:02 AM

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



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