1
Q
• The average value of a function on an interval is the area under the curve divided by the length of the interval.
A
• The average value of a function on an interval is the area under the curve divided by the length of the interval.
2
Q
• Average value = 1/(b-a) lim(B->A) f(x)dx.
A
• Average value = 1/(b-a) lim(B->A) f(x)dx.
AP Calculus AB
flashcards
Decks in class (169)
# Cards
-
An Introduction to Thinkwell Calculus (1.1.1)2
-
The Two Questions of Calculus (1.1.2)2
-
Average Rates of Change (1.1.3)2
-
How to Do Math (1.1.4)1
-
Functions (1.2.1)3
-
Graphing Lines (1.2.2)3
-
Parabolas (1.2.3)3
-
Some Non-Euclidean Geometry (1.2.4)1
-
Finding Rate of Change over an Interval (2.1.1)2
-
Finding Limits Graphically (2.1.2)2
-
The Formal Definition of a Limit (2.1.3)2
-
The Limit Laws, Part I (2.1.4)1
-
The Limit Laws, Part II (2.1.5)2
-
One-Sided Limits (2.1.6)3
-
The Squeeze Theorem (2.1.7)3
-
Continuity and Discontinuity (2.1.8)2
-
Evaluating Limits (2.2.1)3
-
Limits and Intermediate Forms (2.2.2)3
-
Two Techniques for Evaluating Limits (2.2.3)2
-
On Overview of Limits (2.2.4)2
-
Rates of Change, Secants, and Tangents (3.1.1)4
-
Finding Instantaneous Velocity (3.1.2)4
-
The Derivative (3.1.3)3
-
Differentiability (3.1.4)2
-
The Slope of a Tangent Line (3.2.1)2
-
Instantaneous Rate (3.2.2)2
-
The Equation of a Tangent Line (3.2.3)2
-
More on Instantaneous Rate (3.2.4)2
-
The Derivative of the Reciprocal Function (3.3.1)2
-
The Derivative of the Square Root Function (3.3.2)3
-
A Shortcut for Finding Derivatives (4.1.1)2
-
A Quick Proof of the Power Rule (4.1.2)2
-
Uses of the Power Rule (4.1.3)3
-
The Product Rule (4.2.1)2
-
The Quotient Rule (4.2.2)2
-
An Introduction to the Chain Rule (4.3.1)2
-
Using the Chain Rule (4.3.2)2
-
Combining Computational Techniques (4.3.3)2
-
A Review of Trigonometry (5.1.1)2
-
Graphic Trigonometric Functions (5.1.2)3
-
The Derivatives of Trigonometric Functions (5.1.3)2
-
The Number Pi (5.1.4)3
-
Graphing Exponential Functions (5.2.1)2
-
Derivatives of Exponential Functions (5.2.2)2
-
Evaluating Logarithmic Functions (5.3.1)3
-
The Derivative of the Natural Log Function (5.3.2)2
-
Using the Derivative Rules with Transcendental Functions (5.3.3)2
-
An Introduction to Implicit Differentiation (6.1.1)2
-
Finding the Derivative Implicitly (6.1.2)2
-
Using Implicit Differentiation (6.2.1)1
-
Applying Implicit Differentiation (6.2.2)2
-
The Exponential and Natural Log Functions (6.3.1)3
-
Differentiating Logarithmic Functions (6.3.2)3
-
Logarithmic Differentiation (6.3.3)3
-
The Basics of Inverse Functions (6.3.4)3
-
Finding the Inverse of a Function (6.3.5)2
-
Derivatives of Inverse Functions (6.4.1)1
-
The Inverse Sine, Cosine, and Tangent Functions (6.5.1)2
-
The Inverse Secant, Cosecant, and Cotangent Functions (6.5.2)1
-
Evaluating Inverse Trigonometric Functions (6.5.3)2
-
Derivatives of Inverse Trigonometric Functions (6.6.1)1
-
Defining the Hyperbolic Functions (6.7.1)2
-
Hyperbolic Identities (6.7.2)3
-
Derivatives of Hyperbolic Functions (6.7.3)2
-
Acceleration and the Derivative (7.1.1)2
-
Solving Word Problems Involving Distance and Velocity (7.1.2)3
-
High-Order Derivatives and Linear Approximation (7.2.1)2
-
Using the Tangent Line Approximation Formula (7.2.2)1
-
Newton's Method (7.2.3)1
-
The Connection between Slope and Optimization (7.3.1)2
-
The Fence Problem (7.3.2)2
-
The Box Problem (7.3.3)1
-
The Can Problem (7.3.4)2
-
The Wire-Cutting Problem (7.3.5)3
-
The Pebble Problem (7.4.1)2
-
The Ladder Problem (7.4.2)2
-
The Baseball Problem (7.4.3)3
-
The Blimp Problem (7.4.4)2
-
Math Anxiety (7.4.5)1
-
An Introduction to Curve Sketching (8.1.1)2
-
Three Big Theorems (8.1.2)3
-
Morale Moment (8.1.3)1
-
Critical Points (8.2.1)2
-
Maximum and Minimum (8.2.2)3
-
Regions Where a Function Increases or Decreases (8.2.3)2
-
The First Derivative Test (8.2.4)3
-
Math Magic (8.2.5)1
-
Concavity and Inflection Points (8.3.1)3
-
Using the Second Derivative to Examine Concavity (8.3.2)2
-
The Möbius Band (8.3.4)1
-
Graphs of Polynomial Functions (8.4.1)2
-
Cusp Points and the Derivative (8.4.2)2
-
Domain-Restricted Functions and the Derivative (8.4.3)3
-
The Second Derivative Test (8.4.4)3
-
Vertical Asymptotes (8.5.1)3
-
Horizontal Asymptotes and Infinite Limits (8.5.2)3
-
Graphing Functions with Asymptotes (8.5.3)3
-
Functions with Asymptotes and Holes (8.5.4)3
-
Functions with Asymptotes and Critical Points (8.5.5)3
-
Antidifferentiation (9.1.1)3
-
Antiderivatives of Powers of x (9.1.2)3
-
Antiderivatives of Trigonometric and Exponential Functions (9.1.3)2
-
Undoing the Chain Rule (9.2.1)2
-
Integrating Polynomials by Substitution (9.2.2)2
-
Integrating Composite Trigonometric Functions by Substitution (9.3.1)2
-
Integrating Composite Exponential and Rational Functions by Substitution (9.3.2)2
-
More Integrating Trigonometric Functions by Substitution (9.3.3)2
-
Choosing Effective Function Decompositions (9.3.4)2
-
Approximating Areas of Plane Regions (9.4.1)2
-
Areas, Riemann Sums, and Definite Integrals (9.4.2)3
-
The Fundamental Theorem of Calculus, Part 1 (9.4.3)2
-
The Fundamental Theorem of Calculus, Part II (9.4.4)3
-
Illustrating the Fundamental Theorem of Calculus (9.4.5)3
-
Evaluating Definite Integrals (9.4.6)3
-
An Overview of Trigonometric Substitution Strategy (9.5.1)1
-
Trigonometric Substitution Involving a Definite Integral: Part One (9.5.2)1
-
Trigonometric Substitution Involving a Definite Integral: Part Two (9.5.3)2
-
Deriving the Trapezoidal Rule (9.6.1)1
-
An Example of the Trapezoidal Rule (9.6.2)1
-
Antiderivatives and Motion (10.1.1)5
-
Gravity and Vertical Motion (10.1.2)3
-
Solving Vertical Motion Problems (10.1.3)2
-
The Area between Two Curves (10.2.1)2
-
Limits of Area and Integration (10.2.2)1
-
Common Mistakes to Avoid When Finding Areas (10.2.3)2
-
Regions Bound by Several Curves (10.2.4)1
-
Finding Areas by Integrating with Respect to y: Part One (10.3.1)2
-
Finding Areas by Integrating with Respect to y: Part Two (10.3.2)2
-
Area, Integration by Substitution, and Trigonometry (10.3.3)2
-
Finding the Average Value of a Function (10.4.1)2
-
Finding Volumes Using Cross-Sectional Slices (10.5.1)2
-
An Example of Finding Cross-Sectional Volumes (10.5.2)2
-
Solids of Revolution (10.6.1)2
-
The Disk Method along the y-Axis (10.6.2)2
-
A Transcendental Example of the Disk Method (10.6.3)2
-
The Washer Method across the x-Axis (10.6.4)2
-
The Washer Method across the y-Axis (10.6.5)2
-
Introducing the Shell Method (10.7.1)1
-
Why Shells Can Be Better Than Washers (10.7.2)2
-
The Shell Method: Integrating with Respect to y (10.7.3)1
-
An Introduction to Work (10.8.1)3
-
Calculating Work (10.8.2)2
-
Hooke's Law (10.8.3)2
-
Center of Mass (10.9.1)3
-
The Center of Mass of a Thin Plate (10.9.2)2
-
An Introduction to Arc Length (10.10.1)2
-
Finding Arc Lengths of Curves Given by Functions (10.10.2)1
-
An Introduction to Differential Equations (11.1.1)2
-
Solving Separable Differential Equations (11.1.2)2
-
Finding a Particular Solution (11.1.3)1
-
Direction Fields (11.1.4)2
-
Euler's Method for Solving Differential Equations Numerically (11.1.5)2
-
Exponential Growth (11.2.1)1
-
Logistic Growth (11.2.2)4
-
Radioactive Decay (11.2.3)2
-
Indeterminate Forms (12.1.1)2
-
An Introduction to L'Hôpital's Rule (12.1.2)2
-
Basic Uses of L'Hôpital's Rule (12.1.3)3
-
More Exotic Examples of Indeterminate Forms (12.1.4)3
-
L'Hôpital's Rule and Indeterminate Products (12.2.1)2
-
L'Hôpital's Rule and Indeterminate Differences (12.2.2)2
-
L'Hôpital's Rule and One to the Infinite Power (12.2.3)2
-
Another Example of One to the Infinite Power (12.2.4)2
-
The First Type of Improper Integral (12.3.1)3
-
The Second Type of Improper Integral (12.3.2)1
-
Infinite Limits of Integration, Convergence, and Divergence (12.3.3)1
-
An Introduction to Paradoxes (13.1.1)1
-
Paradoxes and Air Safety (13.1.2)1
-
A Glimpse Into Calculus II (13.3.1)2
