AP Calculus AB — Fundamental Concepts

Front

What is the formal definition of a limit?

Back

If f(x) becomes arbitrarily close to a unique number L as x approaches c (from either side), then L is the limit. Algebraically, we write lim_{x->c} f(x) = L.

Front

Removable Discontinuity

Back

A 'hole' in a graph where the limit exists, but the function value is either undefined or not equal to the limit. It can be 'removed' by redefining f(c) to match the limit.

Front

Intermediate Value Theorem (IVT)

Back

If f is continuous on [a, b] and k is any number between f(a) and f(b), then there exists at least one number c in [a, b] such that f(c) = k. This guarantees solutions exist within intervals.

Front

Definition of Continuity at a Point

Back

A function f is continuous at x = c if three conditions are met: 1) f(c) is defined, 2) lim_{x->c} f(x) exists, and 3) lim_{x->c} f(x) = f(c).

Front

Vertical Asymptotes

Back

Vertical lines x = a where the function increases or decreases without bound. This occurs when the limit of the function is infinity (positive or negative) as x approaches a from the left or right.