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February 28th, 2013, 10:36 PM   #1
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Stuck on an improper integral problem

My friend and I are completely stuck on this problem. When I get to the point to take the limit as t->infinity it would come out to ln|infinity/infinity| and that doesn't "work" right? We are just really confused. If someone could help explain that would be great.

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March 1st, 2013, 12:07 AM   #2
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Re: Stuck on an improper integral problem

You have correctly derived:



As we observe that hence:

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March 1st, 2013, 08:27 AM   #3
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Re: Stuck on an improper integral problem

Thanks! Now that I see what you did it's like "duh!"

I think the part that was confusing us was taking the limit as t->infinity of ln|t/(2t+1)|. Just to clarify, you used l'H˘pital's rule to get 1/2, correct?
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March 1st, 2013, 09:56 AM   #4
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Re: Stuck on an improper integral problem

While you can use L'H˘pital's rule, you could also rewrite the expression by dividing each term in the numerator and denominator by t:

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