# A question about uniform continuity (analysis)

1. Dec 16, 2012

### Artusartos

1. The problem statement, all variables and given/known data

For question 19.2 in this link:

http://people.ischool.berkeley.edu/~johnsonb/Welcome_files/104/104hw7sum06.pdf [Broken]

I came up with a different proof, but I'm not sure if it is correct...

2. Relevant equations

3. The attempt at a solution

Let $$|x-y|< \delta$$

For $$|f(x)-f(y)| = |x^2 - x^y| = |x-y||x+y| < \delta|x+y|$$, we know that the largest that |x+y| can be is 6. So if we let $$\delta= \epsilon/6$$...

We will have

$$|f(x)-f(y)| = |x^2 - x^y| = |x-y||x+y| < \delta|x+y| < (\epsilon/6)(6) = \epsilon$$

If this is true for the largest possibility, then it must be possible for all of them...

Do you think my answer is correct, or is there something that I'm missing?