Labs

Introducing Calculus: Can Change Occur at an Instant?

Defining Limits and Using Limit Notation

Estimating Limit Values from Graphs

Estimating Limit Values from Tables

Determining Limits Using Algebraic Manipulation

Connecting Multiple Representations of Limits

Exploring Types of Discontinuities

Defining Continuity at a Point

Removing Discontinuities

Connecting Infinite Limits and Vertical Asymptotes

Connecting Limits at Infinity and Horizontal Asymptotes

Working with the Intermediate Value Theorem (IVT)

Defining Average and Instantaneous Rates of Change at a Point

Defining the Derivative of a Function and Using Derivative Notation

Estimating Derivatives of a Function at a Point

Implicit Differentiation

Straight-Line Motion: Connecting Position, Velocity, and Acceleration

Introduction to Related Rates

Solving Related Rates Problems

Introduction to Optimization Problems

Solving Optimization Problems

Exploring Behaviors of Implicit Relations

Exploring Accumulations of Change

Approximating Areas with Riemann Sums

Riemann Sums, Summation Notation, and Definite Integral Notation

The Fundamental Theorem of Calculus and Accumulation Functions

Interpreting the Behavior of Accumulation Functions Involving Area

Applying Properties of Definite Integrals

The Fundamental Theorem of Calculus and Definite Integrals

Integrating Using Substitution

Selecting Techniques for Antidifferentiation

Sketching Slope Fields

Reasoning Using Slope Fields

Exponential Models with Differential Equations

Connecting Position, Velocity, and Acceleration of Functions Using Integrals

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