► My Limits & Continuity course: https://www.kristakingmath.com/limits-and-continuity-course
The precise definition of the limit, also called the epsilon-delta definition, is the proof of the concept of the limit. It proves the limit because it shows how, as you move closer and closer to a particular value of x, the value of the function will move closer and closer to a particular value of y.
If you want to use technical terms, what you're doing is limiting the value of delta, which is the distance you can move away from x, in order to limit the value of epsilon, which is the distance you can move away from the corresponding value along the y-axis.
To sum it up, if you found the limit some other way using calculus (like with substitution, factoring, conjugate method, L'Hospital's rule, etc.), this is the theorem that would let you prove that the value of the limit you already found is actually legitimate. It tells you why the calculus works how it does.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com
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Tagged under: limits continuity,educational, ,Krista King,epsilon-delta,calculus,expert,epsilon-delta definition,precise definition limit
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