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June 23rd, 2011, 11:56 AM   #1
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Prove a property in limits

How can I prove that the equality:

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June 23rd, 2011, 12:42 PM   #2
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Re: Prove a property in limits

Quote:
Originally Posted by harkaz2
How can I prove that the equality:

Use this rule:
Assume that both and are defined near and then
Then , if is a positive integer.
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June 24th, 2011, 02:20 AM   #3
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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?
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June 24th, 2011, 06:32 AM   #4
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Re: Prove a property in limits

Quote:
Originally Posted by harkaz2
Well, I have proven that the statement is true for every rational r.
How can I generalise for every r in R?
Won't you get problems for negative r? Example:


is undefined.
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June 24th, 2011, 11:19 AM   #5
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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.
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June 26th, 2011, 11:34 AM   #6
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Re: Prove a property in limits

Proof found! Topic is thus closed.
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