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Unit 1: Limits and Continuity

Limits Overview

Limits Overview

Limit Notation (Left-Hand, Right-Hand, Overall)

Left Hand Limit (LHL)

Right Hand Limit (RHL)

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 1: Left Hand Limit (Video)

Example 2: Right Hand Limit

Example 2: Right Hand Limit (Video)

Example 3: Overall Limit Exists

Example 3: Overall Limit Exists (Video)

Example 4: Overall Limit Does Not Exist

Example 4: Overall Limit Does Not Exist (Video)

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

Example 4: Overall Limit Does Not Exist (Video)

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