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AP Calculus AB
> 1.1.4 How to Do Math > Flashcards
1.1.4 How to Do Math Flashcards
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AP Calculus AB
(190 decks)
1.1.1 An Introduction to Thinkwell Calculus
1.1.2 The Two Questions of Calculus
1.1.3 Average Rates of Change
1.1.4 How to Do Math
1.2.1 Functions
1.2.2 Graphing Lines
1.2.3 Parabolas
1.2.4 Some Non-Euclidean Geometry
Chapter 1 Practice Test
Chapter 1 Test
2.1.1 Finding Rate of Change over an Interval
2.1.2 Finding Limits Graphically
2.1.3 The Formal Definition of a Limit
2.1.4 The Limit Laws, Part I
2.1.5 The Limit Laws, Part II
2.1.6 One-Sided Limits
2.1.7 The Squeeze Theorem
2.1.8 Continuity and Discontinuity
2.2.1 Evaluating Limits
2.2.2 Limits and Indeterminate Forms
2.2.3 Two Techniques for Evaluating Limits
2.2.4 An Overview of Limits
Chapter 2 Practice Test
Chapter 2 Test
3.1.1 Rates of Change, Secants, and Tangents
3.1.2 Finding Instantaneous Velocity
3.1.3 The Derivative
3.1.4 Differentiability
3.2.1 The Slope of a Tangent Line
3.2.2 Instantaneous Rate
3.2.3 The Equation of a Tangent Line
3.2.4 More on Instantaneous Rate
3.3.1 The Derivative of the Reciprocal Function
3.3.2 The Derivative of the Square Root Function
Chapter 3 Practice Test
Chapter 3 Test
4.1.1 A Shortcut for Finding Derivatives
4.1.2 A Quick Proof of the Power Rule
4.1.3 Uses of the Power Rule
4.2.1 The Product Rule
4.2.2 The Quotient Rule
4.3.1 An Introduction to the Chain Rule
4.3.2 Using the Chain Rule
4.3.3 Combining Computational Techniques
Chapter 4 Practice Test
Chapter 4 Test
5.1.1 A Review of Trigonometry
5.1.2 Graphing Trigonometric Functions
5.1.3 The Derivatives of Trigonometric Functions
5.1.4 The Number Pi
5.2.1 Graphing Exponential Functions
5.2.2 Derivatives of Exponential Functions
5.3.1 Evaluating Logarithmic Functions
5.3.2 The Derivative of the Natural Log Function
5.3.3 Using the Derivative Rules with Transcendental Functions
Chapter 5 Practice Test
Chapter 5 Test
6.1.1 An Introduction to Implicit Differentiation
6.1.2 Finding the Derivative Implicitly
6.2.1 Using Implicit Differentiation
6.2.2 Applying Implicit Differentiation
6.3.1 The Exponential and Natural Log Functions
6.3.2 Differentiating Logarithmic Functions
6.3.3 Logarithmic Differentiation
6.3.4 The Basics of Inverse Functions
6.3.5 Finding the Inverse of a Function
6.4.1 Derivatives of Inverse Function
6.5.1 The Inverse Sine, Cosine, and Tangent Functions
6.5.2 The Inverse Secant, Cosecant, and Cotangent Functions
6.5.3 Evaluating Inverse Trigonometric Functions
6.6.1 Derivatives of Inverse Trigonometric Functions
6.7.1 Defining the Hyperbolic Functions
6.7.2 Hyperbolic Identities
6.7.3 Derivatives of Hyperbolic Functions
Chapter 6 Practice Test
Chapter 6 Test
Practice Midterm Exam
Midterm Exam
7.1.1 Acceleration and the Derivative
7.1.2 Solving Word Problems Involving Distance and Velocity
7.2.1 Higher-Order Derivatives and Linear Approximation
7.2.2 Using the Tangent Line Approximation Formula
7.2.3 Newton's Method
7.3.1 The Connection Between Slope and Optimization
7.3.2 The Fence Problem
7.3.3 The Box Problem
7.3.4 The Can Problem
7.3.5 The Wire-Cutting Problem
7.4.1 The Pebble Problem
7.4.2 The Ladder Problem
7.4.3 The Baseball Problem
7.4.4 The Blimp Problem
Chapter 7 Practice Test
Chapter 7 Test
8.1.1 An Introduction to Curve Sketching
8.1.2 Three Big Theorems
8.2.1 Critical Points
8.2.2 Maximum and Minimum
8.2.3 Regions Where a Function Increases or Decreases
8.2.4 The First Derivative Test
8.3.1 Concavity and Inflection Points
8.3.2 Using the Second Derivative to Examine Concavity
8.4.1 Graphs of Polynomial Functions
8.4.2 Cusp Points and the Derivative
8.4.3 Domain-Restricted Functions and the Derivative
8.4.4 The Second Derivative Test
8.5.1 Vertical Asymptotes
8.5.2 Horizontal Asymptotes and Infinite Limits
8.5.3 Graphing Functions with Asymptotes
8.5.4 Functions with Asymptotes and Holes
8.5.5 Functions with Asymptotes and Critical Points
Chapter 8 Practice Test
Chapter 8 Test
9.1.1 Antidifferentiation
9.1.2 Antiderivatives of Powers of x
9.1.3 Antiderivatives of Trigonometric and Exponential Functions
9.2.1 Undoing the Chain Rule
9.2.2 Integrating Polynomials by Substitution
9.3.1 Integrating Composite Trigonometric Functions by Substitution
9.3.2 Integrating Composite Exponential and Rational Functions by Substitution
9.3.3 More Integrating Tirgonometric Functions by Substitution
9.3.4 Choosing Effective Function Decompositions
9.4.1 Approximating Areas of Plane Regions
9.4.2 Areas, Riemann Sums, and Definite Integrals
9.4.3 The Fundamental Theorem of Calculus, Part I
9.4.4 The Fundamental Theorem of Calculus, Part II
9.4.5 Illustrating the Fundamental Theorem of Calculus
9.4.6 Evaluating Definite Integrals
9.5.1 An Overview of Trigonometric Substitution Strategy
9.5.2 Trigonometric Substitution Involving a Definite Integral: Part One
9.5.3 Trigonometric Substitution Involving a Definite Integral: Part Two
9.6.1 Deriving the Trapezoidal Rule
9.6.2 An Example of the Trapezoidal Rule
Chapter 9 Practice Test
Chapter 9 Test
10.1.1 Antiderivatives and Motion
10.1.2 Gravity and Vertical Motion
10.1.3 Solving Vertical Motion Problems
10.2.1 The Area between Two Curves
10.2.2 Limits of Integration and Area
10.2.3 Common Mistakes to Avoid When Finding Areas
10.2.4 Regions Bound by Several Curves
10.3.1 Finding Areas by Integrating with Respect to y: Part One
10.3.2 Finding Areas by Integrating with Respect to y: Part Two
10.3.3 Area, Integration by Substitution, and Trigonometry
10.4.1 Finding the Average Value of a Function
10.5.1 Finding Volumes Using Cross-Sectional Slices
10.5.2 An Example of Finding Cross-Sectional Volumes
10.6.1 Solids of Revolution
10.6.2 The Disk Method along the y-Axis
10.6.3 A Transcendental Example of the Disk Method
10.6.4 The Washer Method across the x-Axis
10.6.5 The Washer Method across the y-Axis
10.7.1 Introducing the Shell Method
10.7.2 Why Shells Can Be Better Than Washers
10.7.3 The Shell Method: Integrating with Respect to y
10.8.1 An Introduction to Work
10.8.2 Calculating Work
10.8.3 Hooke's Law
10.9.1 Center of Mass
10.9.2 The Center of Mass of a Thin Plate
10.10.1 An Introduction to Arc Length
10.10.2 Finding Arc Lengths of Curves Given by Functions
Chapter 10 Practice Test
Chapter 10 Test
11.1.1 An Introduction to Differential Equations
11.1.2 Solving Separable Differential Equations
11.1.3 Finding a Particular Solution
11.1.4 Direction Fields
11.1.5 Euler's Method for Solving Differential Equations Numerically
11.2.1 Exponential Growth
11.2.2 Logistic Growth
11.2.3 Radioactive Decay
Chapter 11 Practice Test
Chapter 11 Test
12.1.1 Indeterminate Forms
12.1.2 An Introduction to L'Hôpital's Rule
12.1.3 Basic Uses of L'Hôpital's Rule
12.1.4 More Exotic Examples of Indeterminate Forms
12.2.1 L'Hôpital's Rule and Indeterminate Products
12.2.2 L'Hôpital's Rule and Indeterminate Differences
12.2.3 L'Hôpital's Rule and One to the Infinite Power
12.2.4 Another Example of One to the Infinite Power
12.3.1 The First Type of Improper Integral
12.3.2 The Second Type of Improper Integral
12.3.3 Infinite Limits of Integration, Convergence, and Divergence
Chapter 12 Practice Test
Chapter 12 Test
Practice Final Exam
Final Exam
