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AP Calculus AB > 1.2.4 Some Non-Euclidean Geometry > Flashcards

1.2.4 Some Non-Euclidean Geometry 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

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

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

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

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

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

Practice 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

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

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

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

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