- Limits – Graphically, limits are range or y-values of a function as you get closer to a particular domain or x- value. If a function approaches different values from both directions, limit is undefined. Limit law of Polynomial functions at a point is the value of the function at that point.
Squeeze(Sandwich Theorem) – If f(x) ≤ g(x) ≤ h(x), when x is close to a and lim (x→a) f(x) = lim (x→a)h(x) = L, then lim (x→a)g(x) = L
Continuous Function – Has no breaks or holes. 3 conditions must be satisfied for a point:
- The function must be defined
- The limit of the function must exist.
- The function and the limit must be equal.
If a function is differentiable(has a derivative), then it is continuous.
Discontinuous Function – Jump(Left and Right hand limits do not agree(piecewise or greatest integer function))or Point(limit exists but disagrees with the function(Rational or piecewise))
Solving Limits – First substitute. If 0/0(indeterminate) form, then factor.