Given the function: f: (0,1) => (2x+1,4x)

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Discussion Overview

The discussion revolves around finding the supremum of the Euclidean norm of the function f: (0,1) => (2x+1,4x). Participants are attempting to determine the correct supremum value and clarify misunderstandings regarding the calculations involved.

Discussion Character

  • Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant asks for clarification on what others are struggling with, suggesting the problem seems straightforward.
  • Another participant expresses uncertainty about their calculated supremum, initially stating it as 6.
  • A subsequent reply challenges the correctness of the 6 value, proposing that the supremum might actually be in the range (0,6).
  • Another participant corrects their earlier claim, stating the supremum should be (0,5) instead of (0,6), asserting that the supremum is 5.
  • One participant argues that both components of the function are increasing as x approaches 1, implying that the limit approaches (3, 4).
  • A later reply suggests that a mistake was made and urges participants to revisit the original post for clarity.

Areas of Agreement / Disagreement

Participants express differing views on the correct supremum value, with some asserting it is 5, while others challenge this conclusion and suggest it may be 6 or in the range (0,6). The discussion remains unresolved with multiple competing views.

Contextual Notes

There are unresolved mathematical steps and assumptions regarding the behavior of the function as x approaches the boundaries of the interval (0,1). The exact calculations leading to the proposed supremum values are not fully detailed.

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

where "E" is for Euclidean norm
 
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What exactly are you stuck on? It looks pretty straightforward...
 


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


evagelos said:
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.
 


I get 6,is it right or wrong??
 


evagelos said:
I get 6,is it right or wrong??

Wrong.
 


LCKurtz said:
Wrong.

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


evagelos said:
Is it not {[tex]||f(x)||_{E}[/tex] :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.
 


LCKurtz said:
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
 
  • #10


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).
 
  • #11


you are making a mistake read the original post again
 

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