Epsilon-Delta Proof Homework: Understanding the Thought Process

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Homework Help Overview

The problem involves an epsilon-delta proof related to limits, specifically demonstrating the relationship between two expressions as a variable approaches a certain value. The original poster expresses a limited understanding of epsilon-delta proofs and seeks insight into the thought processes involved in tackling such problems.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss various approaches to establishing the relationship between δ and ε, with suggestions to start with simple forms of δ, such as δ = kε, and explore other variations like δ = kε² and δ = k√ε. There is also an attempt to manipulate the inequalities to derive conditions for δ based on the given ε.

Discussion Status

The discussion is ongoing, with participants sharing their thought processes and exploring different strategies. Some guidance has been provided regarding potential forms for δ, but there is no explicit consensus on a single approach yet.

Contextual Notes

The original poster's understanding of epsilon-delta proofs is noted as minimal, which may influence the depth of the discussion. The problem setup involves specific inequalities that participants are working to interpret and manipulate.

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Homework Statement



For every ε> 0, there is a δ> 0 such that 1- δ< x <1 + implies 2- ε <7-5x <2 + ε


Homework Equations




The Attempt at a Solution



My understanding of epsilon-delta proofs is very minimal at this point. Was hoping someone would be able to explain your thought process when attempting these kinds of proofs. Thank you!
 
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hi dainty77! :smile:
dainty77 said:
Was hoping someone would be able to explain your thought process when attempting these kinds of proofs.

my thought process would be to attempt the simplest possible solution first …

ie try δ = kε first (for a constant k),

then δ = kε2, then δ = k√ε and so on :wink:
 
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I would start with 2- \epsilon&lt; 7- 5x and see that -5- \epsilon&lt; -5x so that x&lt; 1+ \epsilon/5 and x- 1&lt; \epsilon/5. Then turn to 7- 5x&lt; 2+ \epsilon, so that -5x&lt; -5+ \epsilon and x&gt; 1- \epsilon/5, x- 1&gt; -\epsilon/5. Now do you see what \delta must be?
 
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tiny-tim said:
hi dainty77! :smile:


my thought process would be to attempt the simplest possible solution first …

ie try δ = kε first (for a constant k),

then δ = kε2, then δ = k√ε and so on :wink:

I see where you are gettiing at! Let me work on it some more. Thank you for your help!
 

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