Limits, what they are and what they do

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Limits are foundational in calculus, representing the concept of approaching a specific value. The epsilon-delta definition formalizes this idea, stating that for every epsilon (ε) greater than zero, there exists a delta (δ) such that if x is within δ of a point a (excluding a itself), then f(x) is within ε of the limit L. The discussion highlights the importance of this definition in proving limits rigorously, as well as its application in various techniques, including l'Hospital's rule for evaluating limits. Additionally, the conversation touches on the challenges of proving the non-existence of limits using the epsilon-delta framework. Understanding these concepts is crucial for mastering calculus and its applications.
  • #31
Thanks again

Hi Hurkyl,
By Jove,I think you've got it! Cheers, Jim
 

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