Calculus BC interactive

Adjustable calculus labs (10)

• Unit 1: Limits and Continuity

  Adjustable graph, computed table and explanation in the native lesson.

• Unit 2: Differentiation: Definition and Fundamental Properties

  Adjustable graph, computed table and explanation in the native lesson.

• Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

  Adjustable graph, computed table and explanation in the native lesson.

• Unit 4: Contextual Applications of Differentiation

  Adjustable graph, computed table and explanation in the native lesson.

• Unit 5: Analytical Applications of Differentiation

  Adjustable graph, computed table and explanation in the native lesson.

• Unit 6: Integration and Accumulation of Change

  Adjustable graph, computed table and explanation in the native lesson.

• Unit 7: Differential Equations

  Adjustable graph, computed table and explanation in the native lesson.

• Unit 8: Applications of Integration

  Adjustable graph, computed table and explanation in the native lesson.

• Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions

  Adjustable graph, computed table and explanation in the native lesson.

• Unit 10: Infinite Sequences and Series

  Adjustable graph, computed table and explanation in the native lesson.

Topic retrieval workspaces (111)

• Topic 1.1: 1.1 Introducing Calculus: Can Change Occur at an Instant?

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• Topic 1.2: 1.2 Defining Limits and Using Limit Notation

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• Topic 1.3: 1.3 Estimating Limit Values from Graphs

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• Topic 1.4: 1.4 Estimating Limit Values from Tables

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• Topic 1.5: 1.5 Determining Limits Using Algebraic Properties of Limits

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• Topic 1.6: 1.6 Determining Limits Using Algebraic Manipulation

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• Topic 1.7: 1.7 Selecting Procedures for Determining Limits

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• Topic 1.8: 1.8 Determining Limits Using the Squeeze Theorem

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• Topic 1.9: 1.9 Connecting Multiple Representations of Limits

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• Topic 1.10: 1.10 Exploring Types of Discontinuities

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• Topic 1.11: 1.11 Defining Continuity at a Point

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• Topic 1.12: 1.12 Confirming Continuity over an Interval

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• Topic 1.13: 1.13 Removing Discontinuities

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• Topic 1.14: 1.14 Connecting Infinite Limits and Vertical Asymptotes

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• Topic 1.15: 1.15 Connecting Limits at Infinity and Horizontal Asymptotes

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• Topic 1.16: 1.16 Working with the Intermediate Value Theorem (IVT)

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• Topic 2.1: 2.1 Defining Average and Instantaneous Rates of Change at a Point

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• Topic 2.2: 2.2 Defining the Derivative of a Function and Using Derivative Notation

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• Topic 2.3: 2.3 Estimating Derivatives of a Function at a Point

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• Topic 2.4: 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist

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• Topic 2.5: 2.5 Applying the Power Rule

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• Topic 2.6: 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple

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• Topic 2.7: 2.7 Derivatives of cos x, sin x, e^x, and ln x

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• Topic 2.8: 2.8 The Product Rule

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• Topic 2.9: 2.9 The Quotient Rule

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• Topic 2.10: 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

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• Topic 3.1: 3.1 The Chain Rule

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• Topic 3.2: 3.2 Implicit Differentiation

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• Topic 3.3: 3.3 Differentiating Inverse Functions

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• Topic 3.4: 3.4 Differentiating Inverse Trigonometric Functions

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• Topic 3.5: 3.5 Selecting Procedures for Calculating Derivatives

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• Topic 3.6: 3.6 Calculating Higher-Order Derivatives

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• Topic 4.1: 4.1 Interpreting the Meaning of the Derivative in Context

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• Topic 4.2: 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration

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• Topic 4.3: 4.3 Rates of Change in Applied Contexts Other Than Motion

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• Topic 4.4: 4.4 Introduction to Related Rates

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• Topic 4.5: 4.5 Solving Related Rates Problems

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• Topic 4.6: 4.6 Approximating Values of a Function Using Local Linearity and Linearization

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• Topic 4.7: 4.7 Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms

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• Topic 5.1: 5.1 Using the Mean Value Theorem

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• Topic 5.2: 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

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• Topic 5.3: 5.3 Determining Intervals on Which a Function Is Increasing or Decreasing

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• Topic 5.4: 5.4 Using the First Derivative Test to Determine Relative (Local) Extrema

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• Topic 5.5: 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema

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• Topic 5.6: 5.6 Determining Concavity of Functions over Their Domains

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• Topic 5.7: 5.7 Using the Second Derivative Test to Determine Extrema

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• Topic 5.8: 5.8 Sketching Graphs of Functions and Their Derivatives

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• Topic 5.9: 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative

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• Topic 5.10: 5.10 Introduction to Optimization Problems

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• Topic 5.11: 5.11 Solving Optimization Problems

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• Topic 5.12: 5.12 Exploring Behaviors of Implicit Relations

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• Topic 6.1: 6.1 Exploring Accumulations of Change

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• Topic 6.2: 6.2 Approximating Areas with Riemann Sums

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• Topic 6.3: 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation

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• Topic 6.4: 6.4 The Fundamental Theorem of Calculus and Accumulation Functions

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• Topic 6.5: 6.5 Interpreting the Behavior of Accumulation Functions Involving Area

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• Topic 6.6: 6.6 Applying Properties of Definite Integrals

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• Topic 6.7: 6.7 The Fundamental Theorem of Calculus and Definite Integrals

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• Topic 6.8: 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation

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• Topic 6.9: 6.9 Integrating Using Substitution

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• Topic 6.10: 6.10 Integrating Functions Using Long Division and Completing the Square

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• Topic 6.11: 6.11 Integrating Using Integration by Parts

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• Topic 6.12: 6.12 Integrating Using Linear Partial Fractions

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• Topic 6.13: 6.13 Evaluating Improper Integrals

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• Topic 6.14: 6.14 Selecting Techniques for Antidifferentiation

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• Topic 7.1: 7.1 Modeling Situations with Differential Equations

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• Topic 7.2: 7.2 Verifying Solutions for Differential Equations

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• Topic 7.3: 7.3 Sketching Slope Fields

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• Topic 7.4: 7.4 Reasoning Using Slope Fields

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• Topic 7.5: 7.5 Approximating Solutions Using Euler’s Method

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• Topic 7.6: 7.6 Finding General Solutions Using Separation of Variables

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• Topic 7.7: 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables

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• Topic 7.8: 7.8 Exponential Models with Differential Equations

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• Topic 7.9: 7.9 Logistic Models with Differential Equations

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• Topic 8.1: 8.1 Finding the Average Value of a Function on an Interval

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• Topic 8.2: 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals

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• Topic 8.3: 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts

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• Topic 8.4: 8.4 Finding the Area Between Curves Expressed as Functions of x

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• Topic 8.5: 8.5 Finding the Area Between Curves Expressed as Functions of y

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• Topic 8.6: 8.6 Finding the Area Between Curves That Intersect at More Than Two Points

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• Topic 8.7: 8.7 Volumes with Cross Sections: Squares and Rectangles

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• Topic 8.8: 8.8 Volumes with Cross Sections: Triangles and Semicircles

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• Topic 8.9: 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis

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• Topic 8.10: 8.10 Volume with Disc Method: Revolving Around Other Axes

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• Topic 8.11: 8.11 Volume with Washer Method: Revolving Around the x- or y-Axis

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• Topic 8.12: 8.12 Volume with Washer Method: Revolving Around Other Axes

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• Topic 8.13: 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled

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• Topic 9.1: 9.1 Defining and Differentiating Parametric Equations

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• Topic 9.2: 9.2 Second Derivatives of Parametric Equations

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• Topic 9.3: 9.3 Finding Arc Lengths of Curves Given by Parametric Equations

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• Topic 9.4: 9.4 Defining and Differentiating Vector-Valued Functions

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• Topic 9.5: 9.5 Integrating Vector-Valued Functions

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• Topic 9.6: 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions

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• Topic 9.7: 9.7 Defining Polar Coordinates and Differentiating in Polar Form

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• Topic 9.8: 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

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• Topic 9.9: 9.9 Finding the Area of the Region Bounded by Two Polar Curves

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• Topic 10.1: 10.1 Defining Convergent and Divergent Infinite Series

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• Topic 10.2: 10.2 Working with Geometric Series

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• Topic 10.3: 10.3 The nth Term Test for Divergence

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• Topic 10.4: 10.4 Integral Test for Convergence

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• Topic 10.5: 10.5 Harmonic Series and p-Series

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• Topic 10.6: 10.6 Comparison Tests for Convergence

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• Topic 10.7: 10.7 Alternating Series Test for Convergence

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• Topic 10.8: 10.8 Ratio Test for Convergence

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• Topic 10.9: 10.9 Determining Absolute or Conditional Convergence

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• Topic 10.10: 10.10 Alternating Series Error Bound

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• Topic 10.11: 10.11 Finding Taylor Polynomial Approximations of Functions

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• Topic 10.12: 10.12 Lagrange Error Bound

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• Topic 10.13: 10.13 Radius and Interval of Convergence of Power Series

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• Topic 10.14: 10.14 Finding Taylor or Maclaurin Series for a Function

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• Topic 10.15: 10.15 Representing Functions as Power Series

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Retained source study widgets (65)

These remain in their original readings. Source review states and enrichment scope are retained.

• Graph 7-3-1

  Gallery steps and all-frame reading. Retained source context; follow its local scope and review notes.

• Review 1.2

  Source quiz · reviewed and unfinished items labeled in context. Retained source context; follow its local scope and review notes.

• Gallery 1.1 Bell Curve for Example 7.3.1

  Gallery steps and all-frame reading. Retained source context; follow its local scope and review notes.

• Review 1.3

  Source quiz · reviewed and unfinished items labeled in context. Retained source context; follow its local scope and review notes.

• Review 1.1

  Source quiz · reviewed and unfinished items labeled in context. Retained source context; follow its local scope and review notes.

• Graph 4.3.1

  Figure and selectable notes. Retained source context; follow its local scope and review notes.

• Graph 4.3.2

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• Review 1.3

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• Graph 4.1.1

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• Graph 4.1.2

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• Graph 4.1.3

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• Review 1.1

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• Graph 4.2.1

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• Graph 4.2.2

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• Review 1.2

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• Absolute Convergence and Example 5.2.1

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• Conditional Convergence and Example 5.2.2

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• Review 1.2 Absolute and Conditional Convergence

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• Supplementary Graph for Example 5.1.2

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• Review 1.1 Alternating Series and the Alternating Series Test

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• Supplementary Image for Example 5.3.2

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• Review 1.3 Reimann Rearrangement Theorem

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• Interactive 1.1 Example Problem 8.1.3

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• Review 1.1 Implicit Differentiation

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• Gallery 1.1 Solutions to Differential Equations

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• Review 1.2 Ordinary Differential Equations

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• Gallery 1.2 Looking at partial derivatives

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• Review 1.4 Partial Derivatives

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• Review 1.3 Separable Differential Equations

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• Supplementary Image to Example 8.3.3

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• Graph of the integral in Example 1.5.2

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• Pop Quiz 1.5.1 Improper Integrals

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• Visualizing Integration by Parts

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• Pop Quiz 1.2.1 Integration by Parts

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• Supplemental Image for Example 1.4.2

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• Pop Quiz 1.4.1 Parametric Equations

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• A slightly more visual solution to Example 1.3.1

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• Pop Quiz 1.3.1 Partial Fractions

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• Triangle used in Example 1.1.2

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• Pop Quiz 1.1.1 Trigonometric Substitution

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• Interactive 2.1

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• Interactive 2.2

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• Review 2.3

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• Landing Positions of the Frog

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• Review 2.4

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• Review 2.2

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• Sequence an = 2n-1

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• Graph 2.1.5

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• Graph 2.1.8

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• Review 2.1

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• Graphing and Approximating with a Fourier Series

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• Pop Quiz 1.4.1 Fourier Series

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• Supplemental Image for Example 3.1.2 and 3.1.3

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• Pop Quiz 1.1.1 Geometric Series

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• Supplemental Image for Example 3.2.1

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• Pop Quiz 1.2.1

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• A Representation of the Harmonic Series

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• Pop Quiz 1.3.1 Harmonic Series

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• Interactive 1.1

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• Supplementary image for Example 6.3.3

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• Review 1.3 Maclauren Series

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• A Power Series in Disguise

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• Review 1.1 Power Series

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• Supplementary Image for Example 6.1.2

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• Review 1.2 Taylor Series

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