supremum

[evagelos]

Given the function: f: (0,1) => (2x+1,4x) ,find sup{||f(x)||_{E} :xε(0,1)}

where "E" is for Euclidean norm

[LCKurtz]

What exactly are you stuck on? It looks pretty straightforward...

[evagelos]

What exactly are you stuck on? It looks pretty straightforward...
What do you get for the supremum?

[LCKurtz]

What do you get for the supremum?

What did you get? The idea here is for you to show us what you have done and we will help you over any trouble spots or verify your work.

[evagelos]

I get 6,is it right or wrong??

[LCKurtz]

I get 6,is it right or wrong??

Wrong.

[evagelos]

Wrong.

Is it not {||f(x)||_{E} :xε(0,1)} =(0,6)??

[LCKurtz]

Is it not {||f(x)||_{E} :xε(0,1)} =(0,6)??

No, it isn't. Why don't you show us your work so we can help you find your mistake.

[evagelos]

No, it isn't. Why don't you show us your work so we can help you find your mistake.


Sorry,mistake, it should be : (0,5) instead (0,6) and hence the supremum is 5

[HallsofIvy]

What should be "(0, 5)"???

It looks obvious to me that both components are increasing functions of x and that, as x approaches 1, (2x+1, 4x) approaches (3, 4).

[evagelos]

you are making a mistake read the original post again