AP®︎ Calculus BC Unit 1: Notes & Study Guide
Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 1 of AP Calculus BC – Limits and Continuity.
Unit 1: Limits and Continuity
Explore how limits help analyze change, continuity, and asymptotic behavior.
Begin with Topic 1.1: Introducing Calculus: Can...To review Unit 1, go through each of the 16 topics below.
Everything you actually need to know for your Unit 1 test, pulled directly from the AP® Calculus BC curriculum.
Introducing Calculus: Can Change Occur at an Instant?
Introducing Calculus: Can Change Occur at an Instant?
- Average Rate of Change and the Secant Line
- Instantaneous Rate of Change and the Tangent Line
- The Limit Idea That Makes This Possible
Defining Limits and Using Limit Notation
Defining Limits and Using Limit Notation
- What a Limit Is
- Limit Notation and One-Sided Limits
- Representing Limits in Different Ways
Estimating Limit Values from Graphs
Estimating Limit Values from Graphs
- What a limit means on a graph
- Estimating limits from a graph
- When a limit does not exist
Estimating Limit Values from Tables
Estimating Limit Values from Tables
- What a Limit Is
- One-Sided Limits
- Estimating a Limit from a Table
Determining Limits Using Algebraic Properties of Limits
Determining Limits Using Algebraic Properties of Limits
- The Algebraic Properties of Limits
- Direct Substitution and When It Works
- One-Sided Limits and Algebra
Determining Limits Using Algebraic Manipulation
Determining Limits Using Algebraic Manipulation
- What Algebraic Manipulation Does to a Limit
- Factoring and Canceling Common Factors
- Rationalizing with Conjugates
Selecting Procedures for Determining Limits
Selecting Procedures for Determining Limits
- The Core Question Behind Every Limit
- The Full Set of Limit Procedures
- A Fast Decision Process
Determining Limits Using the Squeeze Theorem
Determining Limits Using the Squeeze Theorem
- The Squeeze Theorem
- The Trig Bounds You Need
- Classic Example Pattern
Connecting Multiple Representations of Limits
Connecting Multiple Representations of Limits
- What It Means for a Limit to Exist
- Numerical Representation
- Graphical Representation
Exploring Types of Discontinuities
Exploring Types of Discontinuities
- What continuity at a point requires
- Removable discontinuity
- Jump discontinuity
Defining Continuity at a Point
Defining Continuity at a Point
- What It Means for a Function to Be Continuous at \( x = c \)
- The Three Conditions Broken Down
- Seeing Continuity on a Graph
Confirming Continuity over an Interval
Confirming Continuity over an Interval
- What It Means to Be Continuous on an Interval
- Functions That Are Continuous on Their Domains
- Domain Restrictions That Break Continuity
Removing Discontinuities
Removing Discontinuities
- Removable Discontinuities and How to Fix Them
- Algebraic Holes in Rational Functions
- Making Piecewise Functions Continuous at a Boundary
Connecting Infinite Limits and Vertical Asymptotes
Connecting Infinite Limits and Vertical Asymptotes
- Infinite Limits and What They Mean
- Vertical Asymptotes
- How to Find Vertical Asymptotes Algebraically
Connecting Limits at Infinity and Horizontal Asymptotes
Connecting Limits at Infinity and Horizontal Asymptotes
- Limits at Infinity and End Behavior
- Horizontal Asymptotes
- Rational Functions and Degree Rules
Working with the Intermediate Value Theorem (IVT)
Working with the Intermediate Value Theorem (IVT)
- The Intermediate Value Theorem
- What IVT Actually Guarantees
- The Sign Change Case (Most Common Use)
Notes
1 credit used · 5/5 remaining