Unit 1: Limits & Continuity AP Calculus BC (Full Guide 2026)
Last Updated: March 2026
Unit 1 (Limits & Continuity) is the foundation of AP Calculus BC.
If you master this unit, everything else becomes easier — especially derivatives and integrals.
—
📊 Unit Weight in Exam
Limits & Continuity contributes around 4%–7% of the exam, but it is used in almost every other unit.
—
📘 Key Concepts You Must Know
1. What is a Limit?
A limit is the value a function approaches as x approaches a certain number.
- Left-hand limit
- Right-hand limit
- Limit exists if both are equal
—
2. Types of Limits
- Finite limits
- Infinite limits
- Limits at infinity
—
3. Continuity
A function is continuous if:
- f(a) is defined
- Limit exists
- Limit = f(a)
—
📉 Important Formulas & Rules
- Limit laws (sum, product, quotient)
- Squeeze theorem
- Intermediate Value Theorem
👉 Official syllabus:
College Board AP Calculus
—
📊 Sample FRQ (Exam Style)
Evaluate:
lim (x→2) (x² – 4)/(x – 2)
Solution:
- Factor: (x-2)(x+2)
- Cancel (x-2)
- Answer = 4
—
📘 Practice PYQs
- Evaluate limits using algebraic simplification
- Analyze graphs for continuity
- Identify discontinuities
👉 Practice more here:
StudyHelper
—
🚨 Common Mistakes in Unit 1
- Not checking left-hand and right-hand limits
- Forgetting to simplify expressions
- Misinterpreting graphs
👉 Full mistake guide:
Common Mistakes
—
🔥 Best Strategy to Master Unit 1
- Understand concepts (don’t memorize)
- Practice limits daily
- Solve FRQs
—
🔗 Internal Links
—
🚀 Smart Learning Method
Instead of just reading notes, use:
- Practice limits questions
- Get instant feedback
- Improve faster
—
🎯 Final Thoughts
Limits & Continuity may seem simple, but they are the base of calculus.
Master this unit and the rest of the course becomes much easier.
Start practicing now →
StudyHelper.io
