Unit 1 · 0/16 Limits and Continuity
1.1 this Introducing Calculus: Can Change Occur at an Instant? 1.2 opens Defining Limits and Using Limit Notation 1.3 Estimating Limit Values from Graphs 1.4 Estimating Limit Values from Tables 1.5 Determining Limits Using Algebraic Properties of Limits 1.6 Determining Limits Using Algebraic Manipulation 1.7 Selecting Procedures for Determining Limits 1.8 Determining Limits Using the Squeeze Theorem 1.9 Connecting Multiple Representations of Limits 1.10 Exploring Types of Discontinuities 1.11 Defining Continuity at a Point 1.12 Confirming Continuity over an Interval 1.13 Removing Discontinuities 1.14 Connecting Infinite Limits and Vertical Asymptotes 1.15 Connecting Limits at Infinity and Horizontal Asymptotes 1.16 Working with the Intermediate Value Theorem (IVT)
Unit 2 · 0/10 Differentiation: Definition and Fundamental Properties
2.1 Defining Average and Instantaneous Rates of Change at a Point 2.2 Defining the Derivative of a Function and Using Derivative Notation 2.3 Estimating Derivatives of a Function at a Point 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist 2.5 Applying the Power Rule 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple 2.7 Derivatives of cos x, sin x, e^x, and ln x 2.8 The Product Rule 2.9 The Quotient Rule 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
Unit 3 · 0/6 Differentiation: Composite, Implicit, and Inverse Functions
3.1 The Chain Rule 3.2 Implicit Differentiation 3.3 Differentiating Inverse Functions 3.4 Differentiating Inverse Trigonometric Functions 3.5 Selecting Procedures for Calculating Derivatives 3.6 Calculating Higher-Order Derivatives
Unit 4 · 0/7 Contextual Applications of Differentiation
4.1 Interpreting the Meaning of the Derivative in Context 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration 4.3 Rates of Change in Applied Contexts Other Than Motion 4.4 Introduction to Related Rates 4.5 Solving Related Rates Problems 4.6 Approximating Values of a Function Using Local Linearity and Linearization 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms
Unit 5 · 0/12 Analytical Applications of Differentiation
5.1 Using the Mean Value Theorem 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema 5.6 Determining Concavity of Functions over Their Domains 5.7 Using the Second Derivative Test to Determine Extrema 5.8 Sketching Graphs of Functions and Their Derivatives 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative 5.10 Introduction to Optimization Problems 5.11 Solving Optimization Problems 5.12 Exploring Behaviors of Implicit Relations
Unit 6 · 0/14 Integration and Accumulation of Change
6.1 Exploring Accumulations of Change 6.2 Approximating Areas with Riemann Sums 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation 6.4 The Fundamental Theorem of Calculus and Accumulation Functions 6.5 Interpreting the Behavior of Accumulation Functions Involving Area 6.6 Applying Properties of Definite Integrals 6.7 The Fundamental Theorem of Calculus and Definite Integrals 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation 6.9 Integrating Using Substitution 6.10 Integrating Functions Using Long Division and Completing the Square 6.11 Integrating Using Integration by Parts AP Calculus BC 6.12 Integrating Using Linear Partial Fractions (Course at a Glance: "Using Linear Partial Fractions") AP Calculus BC 6.13 Evaluating Improper Integrals AP Calculus BC 6.14 Selecting Techniques for Antidifferentiation
Unit 7 · 0/9 Differential Equations
7.1 Modeling Situations with Differential Equations 7.2 Verifying Solutions for Differential Equations 7.3 Sketching Slope Fields 7.4 Reasoning Using Slope Fields 7.5 Approximating Solutions Using Euler's Method AP Calculus BC 7.6 Finding General Solutions Using Separation of Variables 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables 7.8 Exponential Models with Differential Equations 7.9 Logistic Models with Differential Equations AP Calculus BC
Unit 8 · 0/13 Applications of Integration
8.1 Finding the Average Value of a Function on an Interval 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts 8.4 Finding the Area Between Curves Expressed as Functions of x 8.5 Finding the Area Between Curves Expressed as Functions of y 8.6 Finding the Area Between Curves That Intersect at More Than Two Points 8.7 Volumes with Cross Sections: Squares and Rectangles 8.8 Volumes with Cross Sections: Triangles and Semicircles 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis 8.10 Volume with Disc Method: Revolving Around Other Axes 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis 8.12 Volume with Washer Method: Revolving Around Other Axes 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled AP Calculus BC
Unit 9 · 0/9 Parametric Equations, Polar Coordinates, and Vector-Valued Functions
9.1 Defining and Differentiating Parametric Equations AP Calculus BC 9.2 Second Derivatives of Parametric Equations AP Calculus BC 9.3 Finding Arc Lengths of Curves Given by Parametric Equations AP Calculus BC 9.4 Defining and Differentiating Vector-Valued Functions AP Calculus BC 9.5 Integrating Vector-Valued Functions AP Calculus BC 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions AP Calculus BC 9.7 Defining Polar Coordinates and Differentiating in Polar Form AP Calculus BC 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve AP Calculus BC 9.9 Finding the Area of the Region Bounded by Two Polar Curves AP Calculus BC
Unit 10 · 0/15 Infinite Sequences and Series
10.1 Defining Convergent and Divergent Infinite Series AP Calculus BC 10.2 Working with Geometric Series AP Calculus BC 10.3 The nth Term Test for Divergence AP Calculus BC 10.4 Integral Test for Convergence AP Calculus BC 10.5 Harmonic Series and p-Series AP Calculus BC 10.6 Comparison Tests for Convergence AP Calculus BC 10.7 Alternating Series Test for Convergence AP Calculus BC 10.8 Ratio Test for Convergence AP Calculus BC 10.9 Determining Absolute or Conditional Convergence AP Calculus BC 10.10 Alternating Series Error Bound AP Calculus BC 10.11 Finding Taylor Polynomial Approximations of Functions AP Calculus BC 10.12 Lagrange Error Bound AP Calculus BC 10.13 Radius and Interval of Convergence of Power Series AP Calculus BC 10.14 Finding Taylor or Maclaurin Series for a Function AP Calculus BC 10.15 Representing Functions as Power Series AP Calculus BC
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