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June 23rd, 2011, 11:56 AM  #1 
Newbie Joined: Jun 2011 Posts: 4 Thanks: 0  Prove a property in limits
How can I prove that the equality: 
June 23rd, 2011, 12:42 PM  #2  
Member Joined: Aug 2009 From: Copenhagen, Denmark Posts: 45 Thanks: 0  Re: Prove a property in limits Quote:
Assume that both and are defined near and then Then , if is a positive integer.  
June 24th, 2011, 02:20 AM  #3 
Newbie Joined: Jun 2011 Posts: 4 Thanks: 0  Re: Prove a property in limits
Well, I have proven that the statement is true for every rational r. How can I generalise for every r in R? 
June 24th, 2011, 06:32 AM  #4  
Member Joined: Aug 2009 From: Copenhagen, Denmark Posts: 45 Thanks: 0  Re: Prove a property in limits Quote:
is undefined.  
June 24th, 2011, 11:19 AM  #5 
Newbie Joined: Jun 2011 Posts: 4 Thanks: 0  Re: Prove a property in limits
The problem you mention is not my case. I am talking about this category of limits (I didn't know how to put the x> c notation under the lim symbol in the original post) : where c is real number. The case you mention is when x goes to infinity, somewhat different There is no doubt that the property is true; I have seen it in various textbooks. The problem is how I prove it. Should I use dedekind cuts? Or density of rational numbers is enough to prove it? If anyone could help completing this part of the proof, I would much appreciate it. 
June 26th, 2011, 11:34 AM  #6 
Newbie Joined: Jun 2011 Posts: 4 Thanks: 0  Re: Prove a property in limits
Proof found! Topic is thus closed.


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limits, property, prove 
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