Formal Definition of Limits
Formal Definition of LimitsFor a function f(x),Now, I admit that that's quite a bit to swallow all at once. Shake all those epsilons and deltas from your head and take a step back. The limit is concerned with what f(x) looks like around the point x=a. It says that the limit L is the number such that if you take numbers arbitrarily close to x (or in other words, away from x) that the result of f applied to those numbers must be arbitrarily close to L (or in other words, away from L).if and only if for each positive number, there exists a positive number with the property that for any number x in the domain of the function that satisfies the inequalities
One of the important things is that nowhere does it say anything about the actual value of f(x) at x=a. We don't care what f(a) is. (well, maybe we care, but it still doesn't affect the value of the limit.)