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Unit 1: Limits and Continuity
Limits Overview
Limits Overview
Limit Notation (Left-Hand, Right-Hand, Overall)
Limit Notation
Left Hand Limit (LHL)
Right Hand Limit (RHL)
Overall Limit
Finding Limits Using a Graph
Finding Limits Using a Graph
Finding Limits Using a Graph Examples from Actual AP Exams
Method: Finding Limits of a Graph
Example 1: Left Hand Limit
Example 2: Right Hand Limit
Example 3: Overall Limit Exists
Example 4: Overall Limit Does Not Exist
Finding a Limit Using Equations
Finding Limits Using an Equation
Option 1: Plug it in!
Finding Limits Using Equations Examples from Actual AP Exams
Identifier: Limit Option 1
Method: Limit Option 1
Example 1: Option 1 (Plug it in)
Option 2: Factor and Cancel
Factor and Cancel Limit Examples From Actual AP Exams
Identifier: Factor and Cancel
Method: Factor and Cancel
Example 1: Factor and Cancel
Example 2: Factor and Cancel
Option 3: Complex Fractions
Identifier: Complex Fraction Limits
Method: Complex Fraction Limits
Example 1: Complex Fraction Limit
Option 4: Square Roots
Identifier: Square Root Limits
Method: Square Root Limits
Example 1: Square Root Limits
Option 5: Absolute Value
Absolute Value Limit Examples from Actual AP Exams
Identifier: Absolute Value Limits
Method: Absolute Value Limits
Example 1: Absolute Value Limit
Option 6
Trig Functions Category 1: Simplify then Plug it in
Identifier: Trig Function Limits Category 1
Method: Trig Function Limits Category 1
Example 1: Trig Function Limit Category 1
Example 2: Trig Function Limit Category 1
Option 7
Trig Functions Category 2: Sine Limit Identity
Identifier: Trig Function Category 2
Method: Trig Function Limits Category 2
Example 1: Trig Function Limit Category 2
Option 8
Trig Functions Category 3: Cosine Limit Identity
Identifier: Trig Function Category 3
Method: Trig Function Category 3
Example 1: Trig Function Limit Category 3
Option 9: Vertical Asymptotes (Limits that equal infinity)
Vertical Asymptote Examples from Actual AP Exams
Identifier: Vertical Asymptotes
Method: Vertical Asymptotes
Example 1: Vertical Asymptotes
Example 2: Vertical Asymptotes
Example 3: Vertical Asymptotes
Example 4: Vertical Asymptotes
Option 10: Horizontal Asymptotes (Limits whose x-value is heading towards infinity)
Horizontal Asymptote Examples From Actual AP Exams
Identifier: Horizontal Asymptotes
Method 1: Leading Behavior
Method 2: Dividing by the Highest Power of x
Example 1: Leading Behavior (Top-Heavy)
Example 2: Leading Behavior (Bottom-Heavy)
Example 3: Leading Behavior (Balanced)
Example 4: Dividing by the Highest Power of x (Top-Heavy)
Example 5: Dividing by the Highest Power of x (Bottom-Heavy)
Example 6: Dividing by the Highest Power of x (Balanced)
Example 7: 2 Different Horizontal Asymptotes (Pro Level)
Option 11: Squeeze Theorem (Sandwich Theorem)
Squeeze Theorem Examples from Actual AP Exams
Identifier: Squeeze Theorem
Method: Squeeze Theorem
Example 1: Squeeze Theorem
Continuity
Definition of Continuous Function
Using Definition of Continuity Examples From Actual AP Exams
Determining Continuity: Given a Graph
Determining Continuity Given a Graph Examples from Actual AP Exams
Identifier: Continuity Using a Graph
Method: Continuity Using a Graph
Example 1: Continuity Using a Graph
Determining Continuity: Given an Equation
Determining Continuity of an Equation Examples From Actual AP Exams
Identifier: Continuity Using an Equation
Method: Continuity Using an Equation
Example 1: Continuity Using an Equation
Intermediate Value Theorem
Intermediate Value Theorem Examples from Actual AP Exams
Identifier: Intermediate Value Theorem
Method: Intermediate Value Theorem
Example 1: Intermediate Value Theorem
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Horizontal Asymptote Examples From Actual AP Exams

  1. Unit 1: Limits and Continuity
  2. Option 10: Horizontal Asymptotes (Limits whose x-value is heading towards infinity)
  3. Horizontal Asymptote Examples From Actual AP Exams

Do you want to see where horizontal asymptote (limit at infinity) problems appear on previous AP Calc exams and a video solution for those problems?
I have compiled a comprehensive list here so you don’t have to go looking all over the internet.

MCQ’s

  • 2008 AP Calculus AB MCQ Part A Q1
  • 2008 AP Calculus AB MCQ Part A Q19
  • 2012 AP Calculus AB MCQ Part A Q21
  • 2013 AP Calculus AB MCQ Part A Q12
  • 2014 AP Calculus AB MCQ Part A Q7
  • 2014 AP Calculus AB MCQ Part A Q24
  • 2015 AP Calculus AB MCQ Part A Q14
  • 2015 AP Calculus AB MCQ Part A Q20
  • 2016 AP Calculus AB MCQ Part A Q3
  • 2016 AP Calculus AB MCQ Part A Q7

FRQ’s

  • 2021 AP Calculus AB FRQ Part B Q6b
  • 2022 AP Calculus AB FRQ Part B Q6d
  • 2025 AP Calculus AB FRQ Part A Q1c
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