Is the Converse of the Limit Problem True or False?

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Discussion Overview

The discussion revolves around the validity of the converse of a limit problem in calculus, specifically examining the relationship between the limits of a function and its absolute value. The scope includes theoretical aspects of limits and their properties.

Discussion Character

  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant asserts the need to show that the converse of a limit statement is false, specifically stating that if the limit of the absolute value of a function equals the absolute value of a limit, it does not necessarily imply that the limit of the function itself equals the limit.
  • Another participant clarifies the converse statement that needs to be examined, indicating that it is essential to differentiate between the absolute value of a limit and the limit itself.
  • A suggestion is made that demonstrating a counterexample could effectively show the falsity of the converse statement.
  • There is an exchange about the meaning of absolute value, with one participant confirming that |f(x)| represents the absolute value of the function f(x).
  • One participant expresses uncertainty about how to approach the problem, indicating a lack of initial ideas.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the problem, as there are differing levels of understanding and approaches to demonstrating the falsity of the converse limit statement.

Contextual Notes

There is an indication that the discussion may be limited by participants' varying levels of familiarity with the concepts involved, as well as the need for clear definitions and examples to illustrate the points being debated.

k3n
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limit problem - emergency !

Show that the converse is false

LIM x-->c |f(x)|=|L|
LIM x-->c f(x) = M != L

email me !
 
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We don't do believe in doing others' homework for them. We will help, though.

What ideas do you have ?
 
uhm...right now i have no idea at all
 
What does |x| mean ?
 
|f(x)| = the absolute value of f(x)
 
You started by saying "show that the converse is false" but did say the converse of WHAT. I think you are trying to show that the converse of
"if lim f(x)= L then lim |f(x)|= |L|" is false.

The converse would be "if lim |f(x)|= |L|, then lim f(x)= L"

You can show that a general statement is false by showing one example in which it is false.

Gokul43201's question was not because he didn't know what | | meant. It was a hint that the difference between |L| and L is crucial!
 

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