Showing a limit doesn't exist using Delta/Epsilon

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Homework Help Overview

The discussion revolves around proving that the limit of 1/x as x approaches 0 does not exist, utilizing the delta-epsilon definition of a limit.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the delta-epsilon definition of limits and express uncertainty about how to apply it to disprove the limit's existence. There is an attempt to assume a limit exists and explore implications.

Discussion Status

The discussion is ongoing, with some participants seeking clarification on how to approach the problem. Guidance has been offered regarding the need for the original poster to demonstrate effort before receiving further hints.

Contextual Notes

There are indications of forum rules regarding effort in problem-solving, with a warning issued to one participant about starting multiple threads without sufficient input.

lepton123
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Homework Statement



Prove that the limit as x approaches 0 of 1/x does not exist

Homework Equations


Delta epsilon definition


The Attempt at a Solution


I'm really stuck
 
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Use the following definition:

[tex]\forall L;\exists\epsilon>0;\forall\delta>0;\exists x:|x-a|<\delta and|f(x)-L|<\epsilon[/tex]
 
I know that is the definition for a limit, but I am unsure how to disprove it
 
Well first assume that : [tex]\lim_{x\rightarrow0}\frac{1}{x}=L[/tex]
 
lepton123,
Please read your private mails. You have started two threads without showing any effort. If you continue doing so, it could result in a ban from this forum.

mtayab,
Please, no more hints until lepton123 shows some effort.
 

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