Understanding the Epsilon-Delta Definition of Limit in Calculus

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please guys! some one please help me understand the epsilon-delta definition of limit and the delta nbd concept.
 
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What have you been taught so far?
 
It's actually very simple. What does it intuitively mean when we say that \lim_{x\to p}f(x)=y? It means that if you let x approach p then f(x) will approach y. How to see if that is really the case? Well, if the function f is really going to get closer and closer to y if you let x appoach p closer and closer, then it should be the case that if you specify some small interval \delta containing y you can find an interval around p of length \epsilon such that the function f will map that interval within that deviation, no matter how small you make \delta.
 

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