AP Calculus AB: 1.1.2 The Two Questions of Calculus

AP Calculus AB: 2.1.8 Continuity and Discontinuity

A function is continuous at a point if it’s defined there, its limit exists, and the function’s value equals that limit. Discontinuities occur when one or more of these conditions fail, leading to jump, point (removable), or infinite discontinuities.

AP Calculus AB: 2.1.7 The Squeeze Theorem

The Squeeze Theorem helps find the limit of a function by "squeezing" it between two simpler functions whose limits are known and equal. If the given function is always between those two near a point, then its limit at that point is the same.

AP Calculus AB: 2.1.6 One-Sided Limits

One-sided limits examine a function's behavior from only one direction—left (−) or right (+). A limit exists at a point only if both the left-hand and right-hand limits exist and are equal. If they differ, the overall limit does not exist.

AP Calculus AB: 2.1.4 The Limit Laws, Part I

Limits follow the same arithmetic rules as real numbers. You can add, subtract, multiply, or divide limits (if the denominator isn't zero), and constants can be factored out. These properties simplify evaluating complex expressions involving limits.

AP Calculus AB: 2.1.3 The Formal Definition of a Limit

The formal definition of a limit uses ε (epsilon) and δ (delta) to precisely describe how a function approaches a value. It states that for every ε > 0, there exists a δ > 0 such that when x is within δ of c (but not equal to c), f(x) is within ε of the limit L.

AP Calculus AB: 2.1.2 Finding Limits Graphically

Finding limits graphically involves observing the y-value a function approaches as x gets close to a specific point from both sides. If the left and right sides approach the same value, the limit exists; if they differ, the limit does not exist.