Understanding the Epsilon-Delta Definition of Limit in Calculus

[indra00]

please guys! some one please help me understand the epsilon-delta definition of limit and the delta nbd concept.

 

[EnumaElish]

What have you been taught so far?

 

[Johan de Vries]

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 $$\delta$$.