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.

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📊 Unit Weight in Exam

Limits & Continuity contributes around 4%–7% of the exam, but it is used in almost every other unit.

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📘 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

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2. Types of Limits

• Finite limits
• Infinite limits
• Limits at infinity

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3. Continuity

A function is continuous if:

• f(a) is defined
• Limit exists
• Limit = f(a)

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📉 Important Formulas & Rules

• Limit laws (sum, product, quotient)
• Squeeze theorem
• Intermediate Value Theorem

👉 Official syllabus:
College Board AP Calculus

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📊 Sample FRQ (Exam Style)

Evaluate:

lim (x→2) (x² – 4)/(x – 2)

Solution:

• Factor: (x-2)(x+2)
• Cancel (x-2)
• Answer = 4

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📘 Practice PYQs

• Evaluate limits using algebraic simplification
• Analyze graphs for continuity
• Identify discontinuities

👉 Practice more here:
StudyHelper

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🚨 Common Mistakes in Unit 1

• Not checking left-hand and right-hand limits
• Forgetting to simplify expressions
• Misinterpreting graphs

👉 Full mistake guide:
Common Mistakes

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🔥 Best Strategy to Master Unit 1

1. Understand concepts (don’t memorize)
2. Practice limits daily
3. Solve FRQs

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🔗 Internal Links

• Full Guide
• How to Get a 5
• Study Plan

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🚀 Smart Learning Method

Instead of just reading notes, use:

👉 StudyHelper

• Practice limits questions
• Get instant feedback
• Improve faster

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🎯 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