Unit 3: The Derivative
A. Definition of the derivative
Derivatives Practice Quiz (definition and concept)
B. Differentiability
1. Local linearity
2. Numeric derivatives using the calculator
3. Differentiability and continuity
C. Secant and tangent lines (average versus instantaneous rate of change)
D. Techniques of differentiation
1. Notation
2. Derivatives of polynomial functions
3. Derivatives of trigonometric functions
4. Derivatives of radical functions
E. Derivative rules when combining functions
Guided Notes to Follow Videos (PDF)
Solutions to NOTES from Videos (PDF)
Problems to try on your own (PDF)
1. Power rule
Example 1 (Video) Example 2 (Video) Example 3 (Video) Example 4 (Video) Example 5 (Video)Example 6 (Video) Example 7 (Video) Example 8 (Video) Example 9 (Video)
2. Product Rules
Example 1 (Video) Example 2 (Video) Example 3 (Video) Example 4 (Video)
Example 5 (Video) Example 6 (Video) Example 7 (Video) Example 8 (Video)
3. Quotient Rule
Example 1 (Video) Example 2 (Video) Example 3 (Video) Example 4 (Video)
Example 5 (Video) Example 6 (Video) Example 7 (Video)
4. Chain Rule (Applied across all the rules)
Example 1 (Video) Example 2 (Video) Example 3 (Video) Example 4 (Video) Example 5 (Video)Example 6 (Video) Example 7 (Video) Example 8 (Video) Example 9 (Video)
F. Implicit derivatives
G. Normal lines
H. Related rates
I. Derivatives of logarithmic and exponential functions
Calculus Review of Derivatives
Unit 2: Limits and Continuity
A. Definition of limit
1. Finding limits graphically and numerically
2. Evaluating limits analytically
Finding Limits Using Difference of Cubes (Videos for September 14, 2020)
Finding Limits Using Difference of Cubes II (Videos for September 14, 2020)
Finding Limits Using Common Denominator
Finding Limits Using Conjugates
Finding Limits Involving Trig Functions I
B. Limits at a point
1. Properties of limits
2. Well-known theorems
3. One-sided
4. Two-sided
C. Limits involving infinity
1. Asymptotic behavior
2. End behavior
3. Properties of limits
4. Visualizing limits
D. Continuity
1. Continuous functions
2. Discontinuous functions
a. Removable discontinuity
b. Jump discontinuity (non-removable)
c. Infinite discontinuity (non-removable)
E. Rates of Change
1. Average rate of change
2. Instantaneous rate of change
F. Intermediate Value Theorem
ONLINE LEARNING DAILY RECORD
MONDAY 5/4/20: Please get caught up in your preparation for the AP TEST!
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TUESDAY 5/5/20:
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WEDNESDAY 5/6/20:
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THURSDAY 5/7/20:
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FRIDAY 5/8/20: Catch up day.
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MONDAY 4/27/20: 21 Khan Skills Assigned. Due Saturday by 10:00 pm. REVIEW FOR AP TEST!
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TUESDAY 4/28/20: 21 Khan Skills Assigned. Due Saturday by 10:00 pm. REVIEW FOR AP TEST!
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WEDNESDAY 4/29/20: 21 Khan Skills Assigned. Due Saturday by 10:00 pm. REVIEW FOR AP TEST!
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THURSDAY 4/30/20: 21 Khan Skills Assigned. Due Saturday by 10:00 pm. REVIEW FOR AP TEST!
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FRIDAY 5/1/20: 21 Khan Skills Assigned. Due Saturday by 10:00 pm. REVIEW FOR AP TEST!
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MONDAY 4/20/20: More Examples of the Shell Method. Please watch all the videos and take notes. Then complete the worksheet.
Email the work, please label your email in the subject line Shell Method 2. Due by Tuesday at 3:00 pm.
More of Shell Method Example 1 (video)
More of Shell Method Example 2 (video)
More of Shell Method Example 3 (video)
More of Shell Method Example 4 (video)
More of Shell Method Example 5 (video)
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TUESDAY 4/21/20: A quick review worksheet was sent. Please complete and label your email in the subject line SOLIDS OF REVOLUTION.
Due by Wednesday at 3:00 pm.
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WEDNESDAY 4/22/20: Work of AP REVIEW
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THURSDAY 4/23/20: Examples of Volumes Created by Cross-sections or Slicing. Please watch all the videos and take notes.
Then complete the worksheet. Email the work, please label your email in the subject line Cross-Sections. Due by Friday at 3:00 pm.
Cross-Sections Introduction and Some Basic Formulas (video)
Examples of Cross-Sections Taken Perpendicular to x-axis (video)
Examples of Cross-Sections Taken Perpendicular to y-axis (video)
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FRIDAY 4/24/20: Catch up day.
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MONDAY 4/13/20: No School!
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TUESDAY 4/14/20: Please finish up any Khan that may be left and begin looking at the AP resources from College Board.
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WEDNESDAY 4/15/20: Please watch and take notes on the videos below. Worksheet will follow for tomorrow.
Solids of Revolution Review and Intro to Shell Method (Video)
Solids of Revolution Shell Method: Example 1 (Video)
Solids of Revolution Shell Method: Example 2 (Video)
Solids of Revolution Shell Method: Example 3 (Video)
Solids of Revolution Shell Method: Example 4 (Video)
Solids of Revolution Shell Method: Example 5 (Video)
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THURSDAY 4/15/20: Worksheet sent out as homework.
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FRIDAY 4/15/20:
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MONDAY 4/6/20: Please watch and take notes on the videos below. Then complete the worksheet that was emailed.
The due date will be Tuesday by 3:00 pm. Please label your homework in the subject line of the email as Washer Homework.
Solids of Revolution: Washer Method Example 1 (Video)
Solids of Revolution: Washer Method Example 2 (Video)
Solids of Revolution: Washer Method Example 3 (Video)
Solids of Revolution: Washer Method Example 4 (Video)
Solids of Revolution: Washer Method Example 5 (Video)
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TUESDAY 4/7/20: Please complete the 10 skills and watch the three videos assigned on Khan Academy due date will be Monday by 10:00 pm.
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WEDNESDAY 4/8/20: Please complete the 10 skills and watch the three videos assigned on Khan Academy due date will be Monday by 10:00 pm.
THURSDAY 4/9/20: Please complete the 10 skills and watch the three videos assigned on Khan Academy due date will be Monday by 10:00 pm.
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FRIDAY 4/10/20: NO SCHOOL!
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MONDAY 3/30/20: Students need to look over the material (emails) that were forwarded during break. We will begin the next chapter
in calculus tomorrow.
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TUESDAY 3/31/20: Students need to watch the videos posted below. Complete the worksheet that was sent in an email on notebook paper.
Then take pictures of your work and send ONE email to me with all your work. Due Wednesday 4/1/20
Concept of Average Value of a Function (Video)
Introduction and Concepts of Area Between Curves (Video)
Area Between Curves Example 1 (Video)
Area Between Curves Example 2 (Video)
Area Between Curves Example 3 (Video)
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Wednesday 4/1/20: Another worksheets was emailed. Complete the work. Take a picture of your work.
Then send 1 email of all you work. Please label the work Area between Curves #2. Due Thursday by NOON.
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Thursday - Friday 4/2/20 - 4/3/20: Students should watch videos and complete the worksheet that was sent out in an email. Please
have all the notes taken and the worksheet completed by Monday at noon 4/6/20. I would like a picture of your notes sent via email.
Please label it NOTES and then send a separate email for the worksheet labeled DISC METHOD.
Introduction and Concept for Solids of Revolution: (Video)
Solids of Revolution: Disc Method Example 1 (Video)
Solids of Revolution: Disc Method Example 2 (Video)
Solids of Revolution: Disc Method Example 3 (Video)
Solids of Revolution: Disc Method Example 4 (Video)
Solids of Revolution: Disc Method Example 5 (Video)