AP Calculus AB Exam Review Flashcards

Flashcards for AP Calculus AB exam review, covering key concepts from limits and continuity to applications of integration.

Limit

The value that a function approaches as the input approaches a certain value.

Continuity

A function is continuous if it has no breaks, jumps, or undefined points.

Intermediate Value Theorem

If f(a) and f(b) have opposite signs, there exists a c in (a,b) such that f(c) = 0.

Derivative

The instantaneous rate of change of a function.

Limit Definition of the Derivative

A limit used to define the derivative of a function.

Product Rule

A rule for finding the derivative of a product of two functions.

Quotient Rule

A rule for finding the derivative of a quotient of two functions.

Chain Rule

A rule for differentiating composite functions.

Implicit Differentiation

Differentiating an equation where y is implicitly defined as a function of x.

Velocity

The rate of change of position with respect to time.

Acceleration

The rate of change of velocity with respect to time.

L’Hopital’s Rule

A method for evaluating limits of indeterminate forms.

Mean Value Theorem

If a function is continuous on [a, b], there exists c in (a, b) where f'(c) equals the average rate of change.

Extreme Value Theorem

A continuous function on a closed interval [a, b] must have a maximum and minimum on that interval.

Critical Points

Points where the derivative is zero or undefined.

Riemann Sums and Trapezoids

Approximating the area under a curve using rectangles or trapezoids.

Fundamental Theorem of Calculus

Relates derivatives and integrals; Part 1: derivative of integral, Part 2: evaluates definite integrals.

U-Substitution

A method for finding antiderivatives of composite functions.

Differential Equation

An equation involving derivatives.

Separate and Integrate

Finding general and particular solutions to differential equations.

Slope Fields

A graphical representation of the solutions to a first-order differential equation.

Average Value of a Function

The average y-value of a function over an interval.

Area Between Curves

Finding the area between two curves by integration.

Volumes of Solids of Revolution

Finding the volume of a 3D solid using integration.