AP Calculus BC Quizs

1^st derivative test

• A technique for solving differential equations

• A way to calculate the area under a curve

• A process for determining the concavity of a function

volume of revolution

(washer, vertical axis)

• 2π∫[a,b] y * f(y) dy

• ∫[a,b] f(x) dx

• πr^2h

speed of a particle

• acceleration

• momentum

• displacement

volume of revolution

(disk, horizontal axis)

• 2πrh

• πr²

• (1/3)πr²h

types of improper integrals

• Type II: Discontinuous integrands

• Type III: Non-converging integrals

• Type IV: Bounded integrals

• @@1 + rac{x}{1!} + rac{x^2}{2!} + rac{x^3}{3!} + rac{x^4}{4!} + ext{...}@@

• @@1 + rac{x^2}{2} + rac{x^3}{3} + rac{x^4}{4} + ext{...}@@

• @@1 + x + x^2 + x^3 + x^4 + ext{...}@@

parametric arc length

• The length of a straight line segment between two points.

• The area under a parametric curve.

• The maximum height of a parametric curve.

Mean Value Theorem

• A theorem that applies only to polynomial functions.

• A theorem that guarantees the existence of a point where the derivative equals the average rate of change over an interval.

• A theorem that states that all functions are linear.

What is the Squeeze Theorem?

• A theorem used in geometry

• A principle in probability

• A technique for solving equations

2^nd derivative test

• A technique for finding local maxima and minima

• A way to evaluate limits of functions

• A process for solving differential equations