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| + | I am having trouble starting the first problem. I am not able to determine a way to find a delta function for g(x). So far, I have the |g(x) - g(u)| set up and simplified, but I just don't see how to get delta as a function of epsilon only. Where do I go from here? | ||
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| + | --[[User:Jberlako|Jberlako]] 12:38, 14 April 2010 (UTC) | ||
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| + | Are you talking about number 2? | ||
| + | The function 1/x^2 is a lipschitz function on x,y>=1. Just take absval |1/(x^2)-1/(y^2)| and try to pull out |x-y| then see if you can figure out if what is left is less than a particular value on the interval. It ends up being less than 2 but doesn't take too much to get there. Then for the second interval you can use the continuous extension property. Let (xn)= 1/2^n be a subsequence then just apply the property. Kind of difficult for the first problem. J.Gars | ||
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| + | Is this homework due thursday? | ||
Latest revision as of 10:51, 18 April 2010
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go back to the Discussion Page
I am having trouble starting the first problem. I am not able to determine a way to find a delta function for g(x). So far, I have the |g(x) - g(u)| set up and simplified, but I just don't see how to get delta as a function of epsilon only. Where do I go from here?
--Jberlako 12:38, 14 April 2010 (UTC)
Are you talking about number 2?
The function 1/x^2 is a lipschitz function on x,y>=1. Just take absval |1/(x^2)-1/(y^2)| and try to pull out |x-y| then see if you can figure out if what is left is less than a particular value on the interval. It ends up being less than 2 but doesn't take too much to get there. Then for the second interval you can use the continuous extension property. Let (xn)= 1/2^n be a subsequence then just apply the property. Kind of difficult for the first problem. J.Gars
Is this homework due thursday?
