Showing a limit doesn't exist using Delta/Epsilon

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SUMMARY

The discussion centers on proving that the limit of 1/x as x approaches 0 does not exist using the delta-epsilon definition of limits. The participants emphasize the importance of demonstrating a lack of convergence to a specific limit L. The delta-epsilon definition requires showing that for every epsilon greater than 0, there exists a delta such that the condition |f(x) - L| < epsilon cannot be satisfied as x approaches 0. The conversation highlights the necessity for participants to show effort in their problem-solving approach.

PREREQUISITES
  • Understanding of the delta-epsilon definition of limits
  • Familiarity with the concept of limits in calculus
  • Basic knowledge of mathematical proofs
  • Experience with functions and their behaviors near discontinuities
NEXT STEPS
  • Study the delta-epsilon definition of limits in detail
  • Learn how to construct proofs for limits that do not exist
  • Explore examples of functions with discontinuities
  • Practice proving limits using various functions, particularly rational functions
USEFUL FOR

Students studying calculus, mathematics educators, and anyone interested in understanding the concept of limits and their proofs in mathematical analysis.

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:

\forall L;\exists\epsilon&gt;0;\forall\delta&gt;0;\exists x:|x-a|&lt;\delta and|f(x)-L|&lt;\epsilon
 
I know that is the definition for a limit, but I am unsure how to disprove it
 
Well first assume that : \lim_{x\rightarrow0}\frac{1}{x}=L
 
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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