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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Method: Square Root Limits

Unit 1: Limits and Continuity Option 4: Square Roots Method: Square Root Limits

Rationalize the fraction.

Step 1: Try Option 1: Plug it in

Step 2: Rationalize the square root.

Rationalize means to get rid of the square root. In algebra you were usually asked to rationalize the denominator when dealing with roots. To accomplish this, you will most often either need to multiply by the conjugate of the given square root, or multiply the top and the bottom of the fraction by the square root.

Step 3: Do the multiplication on the piece you are trying to rationalize.

Do NOT do the multiplication between the pieces you are not trying to rationalize.

Step 4: Look to Factor and Cancel.

You will not always need to Factor, but you will almost always need to Cancel.

Step 5: Go back to Option 1: Plug it in

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