Use the formal definition of limits

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SUMMARY

The discussion focuses on using the formal definition of limits in calculus to construct a proof. Participants emphasize the importance of clearly identifying the statement to be proven and logically structuring the argument from the given premises to the conclusion. A coherent proof must demonstrate the truth of the statement through a well-defined logical process. Additionally, a recommended video resource is mentioned to aid in understanding the proof structure.

PREREQUISITES
  • Understanding of calculus concepts, specifically limits.
  • Familiarity with logical argumentation and proof techniques.
  • Basic knowledge of mathematical notation and terminology.
  • Experience with formal definitions in mathematics.
NEXT STEPS
  • Study the formal definition of limits in calculus.
  • Learn about constructing mathematical proofs and logical arguments.
  • Watch the recommended video on proof techniques for limits.
  • Practice writing proofs for various limit statements.
USEFUL FOR

Students studying calculus, mathematics educators, and anyone looking to improve their proof-writing skills in the context of limits.

Student4
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Homework Statement


Use The Formal definition of limits to show
attachment.php?attachmentid=39471&stc=1&d=1317483256.png


Homework Equations


The Formal definition of limits


The Attempt at a Solution



Tried to do it like this, but that was wrong. What do i need to do different?
attachment.php?attachmentid=39472&stc=1&d=1317483656.jpg
 

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What you wrote has little resemblance to a proof. A proof is an argument showing that some statement is true. First, you should identify what statement it is you're trying to prove. Second, and this is key, you need to write a coherent argument where it's logically clear how you started from the givens and reached the conclusion.

You may find this video helpful:

 
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