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## Homework Statement

Is h(x)=x

^{3}+1 uniformly continuous on the set [1,infinity)?

## The Attempt at a Solution

Let [tex]\epsilon[/tex]>0. For each x,y in the set [1,infinity) with |x-y|<[tex]\delta[/tex], we would have |(x

^{3}+1)-(y

^{3}+1)|=|x

^{3}-y

^{3}|

Now how can I show that this is less than epsilon?