Abstract Algebra- Use the definition of uniform continuity to show that the function f(x)=x³ is uniformly...

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Abstract Algebra- Use the definition of uniform continuity to show that the function f(x)=x³ is uniformly...

[From: ] [author: ] [Date: 12-11-10] [Hit: ]

lf(x)-f(y)l = lx³-y³l = lx-yl * lx²+xy+y²land Im stuck...Thanks in advance for your help.-If x, y lie in the set [0,......

...continuous on the set [0,2].

I started with:
lf(x)-f(y)l = lx³-y³l = lx-yl * lx²+xy+y²l and I'm stuck...

Thanks in advance for your help.

-

If x, y lie in the set [0, 2], we have:

|x² + xy + y²|
= x² + xy + y²
<= 2² + 2*2 + 2²
= 12

Thus, |f(x) - f(y)| <= 12|x - y|.

1

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