A question about uniform continuity (analysis)

[Artusartos]

Homework Statement

For question 19.2 in this link:

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

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

Homework Equations

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?

Thanks in advance

 

[mfb]

The last < should be a <=, but apart from that it is fine.