1
Q
• Using the shell method, the volume V of a solid of revolution is given by V=lim(B->A) 2pixh(x)dx, where x is the radius and h(x) is the height of an arbitrary shell.
A
• Using the shell method, the volume V of a solid of revolution is given by V=lim(B->A) 2pixh(x)dx, where x is the radius and h(x) is the height of an arbitrary shell.
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
