Lecture 5 (Calculus) Limits of Functions, Continuity, and Prove lim sin(x)/x = 1

The precise (ε-δ) definition states: lim_{x→c} f(x) = L means that for every ε > 0 there exists δ > 0 such that:

1. A.If |x − c| < ε, then |f(x) − L| < δ
2. B.If |f(x) − L| < ε, then |x − c| < δ
3. C.If |x − c| ≤ δ, then |f(x) − L| ≤ ε
4. D.If 0 < |x − c| < δ, then |f(x) − L| < ε