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