Limits of Functions
Definition
We say if there exists such that , for all such that .
Theorem
The limit if and only if sequence so that we have .
We say limx→af(x)=L if ∀ε>0 there exists δ>0 such that ∣f(x)−L∣<ε, for all x such that ∣x−a∣<δ.
The limit limn→∞f(n)=L if and only if ∀xn sequence so that xn→a we have f(xn)→L.