Unit 1: Limits and Continuity

Limits Overview
Limits Overview
Limit Notation (Left-Hand, Right-Hand, Overall)
Limit Notation
3 Topics
Left Hand Limit (LHL)
Right Hand Limit (RHL)
Overall Limit
Finding Limits Using a Graph
Finding Limits Using a Graph
5 Topics
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!
3 Topics
Identifier: Limit Option 1
Method: Limit Option 1
Example 1: Option 1 (Plug it in)
Option 2: Factor and Cancel
4 Topics
Identifier: Factor and Cancel
Method: Factor and Cancel
Example 1: Factor and Cancel
Example 2: Factor and Cancel
Option 3: Complex Fractions
3 Topics
Identifier: Complex Fraction Limits
Method: Complex Fraction Limits
Example 1: Complex Fraction Limit
Option 4: Square Roots
3 Topics
Identifier: Square Root Limits
Method: Square Root Limits
Example 1: Square Root Limits
Option 5: Absolute Value
3 Topics
Identifier: Absolute Value Limits
Method: Absolute Value Limits
Example 1: Absolute Value Limit
Option 6
Trig Functions Category 1: Simplify then Plug it in
4 Topics
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
3 Topics
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
3 Topics
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)
6 Topics
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)
10 Topics
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)
3 Topics
Identifier: Squeeze Theorem
Method: Squeeze Theorem
Example 1: Squeeze Theorem
Continuity
Definition of Continuous Function
Determining Continuity: Given a Graph
3 Topics
Identifier: Continuity Using a Graph
Method: Continuity Using a Graph
Example 1: Continuity Using a Graph
Determining Continuity: Given an Equation
3 Topics
Identifier: Continuity Using an Equation
Method: Continuity Using an Equation
Example 1: Continuity Using an Equation
Intermediate Value Theorem
3 Topics
Identifier: Intermediate Value Theorem
Method: Intermediate Value Theorem
Example 1: Intermediate Value Theorem
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Identifier: Intermediate Value Theorem

Unit 1: Limits and Continuity Intermediate Value Theorem Identifier: Intermediate Value Theorem
  • You are asked to show that a given y-value exists between two given x-values .

Usually, you are asked to show that you know a zero( y = 0 ) exists on a given interval x-interval , [ a , b ] , but they don’t actually care what the x-value is, just that you know the y-value will occur.

  • You are given a real-world model that is a continuous model (i.e., temperature, height) and asked to show that you absolutely will get a value in between your given end points.
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