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