AP Calculus AB Study Guide

AP Calculus AB study guide flashcards for key concepts, definitions, and essential information.

The AP Calculus AB exam is comprised of multiple-choice questions and free-response questions.

45 multiple-choice questions; 6 free-response questions

Limits and Continuity questions account for % of the AP Calculus AB exam.

10–12%

The limit of a function f as x approaches c is L if f can be made arbitrarily close to L by taking x sufficiently close to c (but not equal to c). If such a value does not exist, we say the limit .

does not exist (DNE)

Calculating limits can involve techniques such as and .

factoring; rationalizing radical expressions

The states that if the graph of a function lies between two functions which share a limit at a certain point, then the in-between function shares that limit as well.

Squeeze Theorem

The value of the limit can fail to exist in a few ways, such as if one or both of the one-sided limits and have different values.

exist

A function is said to be continuous at a point if it meets the following criteria: 1. exists. 2. exists. 3. = f(c).

lim (x→c) f(x); f(c); lim (x→c) f(x)

The Theorem states that if f is continuous on [a,b], then there exists at least one c in (a,b) where f'(c) = (f(b) - f(a)) / (b - a).

Mean Value Theorem

The Derivative of a function is defined as the limit of the average rate of change, which is expressed as .

(f(a+h) - f(a)) / h as h approaches 0

The average value of a function f on an interval [a,b] is given by .

(1/(b-a)) ∫[a to b] f(x) dx

If a differential equation includes a function and one or more of its derivatives, it is called a .

differential equation

The general solution to a differential equation may have infinitely many solutions characterized by a .

constant