Defining Limits Using Limit Notation (LIM-1.A and LIM-1.B)

Estimating Limit Values from Graphs and Tables (LIM-1.C)

Determining  Limits Using Algebraic Properties of Limits (LIM-1.D)

Determining Limits Using Algebraic Manipulation and Squeeze Theorem (LIM-1.E)

Exploring Types of Discontinuities Defining Continuity at a Point (LIM-2.A)

Confirming Continuity over an Interval (LIM-2.B)

Removing Discontinuities (LIM-2.C)

Connecting Infinite Limits and Vertical & Horizontal Asymptotes (LIM-2.D)

Explain the behavior of a function on an interval using the Intermediate Value Theorem (FUN-1.A)

Determining Average and Instantaneous Rates of Change at a Point (CHA-2.A and CHA-2.B)

Defining the Derivative of a Function and Using Derivative Notation (CHA-2.B and CHA-2.C)

Estimating Derivatives of a Function at a Point (CHA-2.D)

Connecting Differentiability and Continuity:  Determining When Derivatives Do and Do Not Exist (FUN-2.A.)

Applying the Power Rule and Derivative Rules:  Constant, Sum, Difference, and Constant Multiple (FUN-3.A.)

The Product and Quotient Rules (FUN-3.B)

Derivatives of cos x, sin x, e^x, and ln x  and Finding the Derivative of Tangent, Cotangent, Secant, and/or Cosecant Functions (FUN-3.A, LIM-3.A. and FUN-3.B)

The Chain Rule (FUN-3.C)

Implicit Differentiation (FUN-3.D)

Differentiating Inverse Functions (FUN-3.E)

Calculating Higher-Order Derivatives (FUN-3.F)

1. Interpreting the Meaning of the Derivative in Context (CHA-3.A)

2. Straight-Line Motion: Connecting Position, Velocity, and Acceleration (CH-3.B)

3. Rates of Change in Applied Contexts Other Than Motion (CHA-3.C)

4. Introduction to Related Rates and Solving Related Rates Problems (CHA-3.D and CHA-3.E)

5. Approximating Values of a Function Using Local Linearity and Linearization (CHA-3.F)

6. Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms (LIM-4.A)

Using the Mean Value Theorem (FUN-1.B)

Extreme Value Theorem, Global Versus Local Extrema, and Critical Points (FUN-1.C)

Determining Intervals on Which a Function Is Increasing or Decreasing (FUN-4.A)

Using the First Derivative Test to Determine Relative (Local) Extrema (FUN-4.A)

Using the Candidates Test to Determine Absolute (Global) Extrema (FUN-4.A)

Determining Concavity of Functions over Their Domains (FUN-4.A)

Using the Second Derivative Test to Determine Extrema (FUN-4.A)

Sketching Graphs of Functions and Their Derivatives and Connecting a Function, Its First Derivative, and Its Second Derivative (FUN-4.A)

Introduction to Optimization Problems (FUN-4.B)

Exploring Accumulations of Change (CHA-4.A)

Approximating Areas with Riemann Sums (LIM-5.A)

Riemann Sums, Summation Notation, and Definite Integral Notation (LIM-5.B, LIM-5.C)

The Fundamental Theorem of Calculus and Accumulation Functions (FUN-5.A)

Interpreting the Behavior of Accumulation Functions Involving Area (FUN-5.A)

Applying Properties of Definite Integrals (FUN-6.A)

The Fundamental Theorem of Calculus and Definite Integrals (FUN-6.B)

Finding Antiderivatives and Indefinite Integrals:  Basic Rules and Notation (FUN-6.C)

Integrating Using Substitution (FUN-6.D)

Integrating Functions Using Long Division and Completing the Square (FUN-6.D)

Modeling Situations with Differential Equations (FUN-7.A)

Verifying Solutions for Differential Equations (FUN-7.B)

Sketching Slope Fields (FUN-7.C)

Reasoning Using Slope Fields (FUN-7.C)

Finding General Solutions Using Separation of Variables (FUN-7.D) 

Finding Particular Solutions Using Initial Conditions and Separation of Variables (FUN-7.E)

Exponential Models with Differential Equations (FUN-7.F)

Find the Average Value of a Function on an Interval (CHA-4.B)

Connecting Position, Velocity, and Acceleration Functions Using Integrals (CHA-4.C)

Using Accumulation Functions and Definite Integrals in Applied Context (CHA-4.D)

Finding the Area Between Curves Expressed as Functions of x (CHA-4.E)

Find the Area Between Curves Expressed as Functions of y (CHA-5.)

Finding the Area Between Curves That Intersect at More than Two Points

Volumes with Cross Sections:  Squares and Rectangles

Volumes with Cross Sections:  Triangles and Semicircles

Volumes with Disc Method:  Revolving Around the x- or y-axis

Volumes with Washer Method:  Revolving Around the x- or y-axis

Volumes with Washer Method:  Revolving Around Other Axes