I don't think that inequality is going to work (take x=2, y=3).
Ok, so we have
Since 8 is the maximum number you can get out of y+x+2 on the interval [0,3], let .
prove g(x)=x^2 + 2x - 5 is uniformly continuous on [0,3].
proof: Let e>0 and choose delta=e/3. If |y-x|< delta and x,y e[0,3] then |g(y)-g(x)| = |(y^2 +2y -5)-(x^2 +2x -5)|=|y^2 -x^2 +2y-2x|=
|y(y+2) - x(x+2)| < 3|y-x| < (3)delta = e.
Did i do the proof right? I get confused when an interval is given such as [0,3]. What is the difference if the interval was [0,3)? How does that effect the proof?