Limits

Explanation:

• Notes | Annotated

  • Khan video: Limits intro

  • Khan article: Limits intro

  • Khan video: Estimating limit values from graphs

  • Khan video: Unbounded limits (other resources will distinguish between unbounded with positive or negative infinity)

  • Khan article: Estimating limit values from graphs

  • Khan video: One-sided limits from graphs

  • Khan video: One-sided limits from graphs: asymptote

  • Khan video: Connecting limits and graphical behavior

  • Khan video: Approximating limits using tables

  • Khan video: Estimating limits from tables

  • Khan article: Using tables to approximate limit values

  • Khan video: One-sided limits from tables

Practice Problems:

• Worksheet | Answers

• Khan exercise: Limits intro

• Khan exercise: Estimating limit values from graphs

• Khan exercise: One-sided limits from graphs

• Khan exercise: Connecting limits and graphical behavior

• Khan exercise: Creating tables for approximating limits

• Khan exercise: Estimating limits from tables

• Khan exercise: One-sided limits from tables

Explanation: 

• Notes | Annotated

• Khan video: Limit properties

• Khan video: Limits of combined functions (graphically)

• Khan video: Limits of combined functions: piecewise functions (graphically)

• Khan video: Limits by direct substitution (explicitly defined equations)

• Khan video: Undefined limits by direct substitution (explicitly defined equations)

• Khan video: Limits of trigonometric functions

Practice Problems:

• Khan exercise: Limits of combined functions: sums and differences (graphically)

• Khan exercise: Limits of combined functions: products and quotients (graphically)

• Khan exercise: Limits by direct substitution (explicitly defined equations)

• Khan exercise: Direct substitution with limits that don't exist (explicitly defined equations)

• Khan exercise: Limits of trigonometric functions

Explanation:

• Notes | Annotated

• Khan video: Limits of piecewise functions

• Khan video: Limits of piecewise functions: absolute value

Practice Problems:

• Worksheet #1 

• Khan exercise: Limits of piecewise functions

Explanation:

• Notes | Annotated

• Khan video: Limits by factoring

Practice Problems:

• Worksheet #1

• Khan exercise: Limits by factoring

Explanation:

• Notes

• Khan video: Introduction to infinite limits

• Khan video: Infinite limits and asymptotes

• Khan video: Analyzing unbounded limits: rational function

• Khan video: Analyzing unbounded limits: mixed function

• Review of the last three lessons: Khan video: Types of discontinuities

Practice Problems:

• Worksheet #1 

• Khan exercise: Infinite limits: graphical

• Khan exercise: Infinite limits: algebraic 

• Khan exercise:  

Explanation:

• Notes | Annotated

• Khan video: Limits by rationalizing (conjugates)

• Khan video: Trig limit using Pythagorean identity

• Khan video: Trig limit using double angle identity

• Khan video: Strategy in finding limits

• Khan article: Strategy in finding limits

• Videos for the entire section:  Hollis video: Calculation of limits (slides 1-7 and 9-11)

Practice:

• Khan exercise: Limits using conjugates (challenging)

• Khan exercise: Limits using trig identities (challenging)

Teacher Resource: ExamView Test Bank (purchase)

Explanation:

• Khan video: Introduction to limits at infinity

• Khan video: Functions with same limit at infinity

Practice:

• Khan exercise: Limits at infinity: graphical

• Worksheet

• Activity

Explanation:

• Notes | Annotated

• Khan video: Limits at infinity of quotients

• Khan video: Limits and Infinity - this video is more about the concept than the procedure for finding the limit of a function as x approaches infinity

• Khan video:  Limits at positive and negative infinity

• Khan video: More limits at infinity - this one has the most examples

• Hollis video: horizontal asymptotes (slides 1-7) 

Practice Problems:

• Worksheet #1 | Answers

• Worksheet #2 | Answers

• Khan Exercises: Limits 2 (includes limits of a function as x approaches a number or infinity)

Explanation:

• Notes | Annotated

• Khan video: Limits with two horizontal asymptotes - this video is more about the concept than the procedures

Practice Problems:

• Worksheet #1 | Answers

• Worksheet #2 | Answers

Explanation:

• Notes | Annotated

Practice Problems

• Worksheet #1 | Answers

• Worksheet #2 | Answers

Practice Problems:

• Different Limits of a Rational Expression WS | Answers

• Limits at a Point and to Infinity Mixed Review WS | Answers

Teacher Resources:

• ExamView Test bank (purchase)

Explanation:

• Notes | Annotated

Practice Problems:

• Worksheet #1 | Answers

• Worksheet #2 | Answers

Explanation:

• Notes | Annotated

• Khan video: Squeeze theorem intro

• Khan video: Limit of sin(x)/x as x approaches 0

• Khan video: Limit of (1-cos(x))/x as x approaches 0

Practice Problems:

• Worksheet #1

• Khan exercises: Squeeze theorem

Explanation:

• Notes

• Desmos Activity: Limits and Continuity (teacher use only)

• Hollis video: Continuity (watch 1-4, 6-9)

Explanation:

• Notes | Annotated

• Desmos Activity: The Intermediate Value Theorem (teacher use only)

• Hollis video: Continuity (slide 10 is IVT)

Explanation: 

• Summary Notes

Practice Problems:

• Worksheet #1 | Answers

• Worksheet #2 | Answers