Model rates of change, including related rates problems.

### Related Rates Problems

by Allen Wolmer

Mooculus Calculus Textbook Sect 8.3 pp 136-142

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### Related Rates

by Allen Wolmer

A Youtube Calculus Workbook (Part 1). A guide through a playlist of instructional Calculus Videos.

Section 7.5-7.8 pp 109-116

The first time you access this link to download the PDF, you will be asked four questions. Any that do not apply to you may be answered using any of the options listed.

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### Related Rates: Intro and Theory

by Allen Wolmer

A Firefly Lectures video on this topic.

Video duration:  10:17

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### Related Rates Example: Falling Ladder

by Allen Wolmer

A Firefly Lectures video on this topic.

Video duration:  10:52

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### Related Rates Example: Water In Trough

by Allen Wolmer

A Firefly Lectures video on this topic.

Video duration:  9:58

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### Related Rates Example: Fill Balloon With Air

by Allen Wolmer

A firefly Lectures video on this topic.

Video duration:  8:36

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### Related Rates in Calculus Part 1

by Allen Wolmer

A Youtube video on this topic. There may be some commercial content at the beginning.

Video duration:  21:00

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### Related Rates Part 2 Linear vs Angular Speed

by Allen Wolmer

A Youtube video on this topic. There may be short commercial content at the beginning.

Video duration:  28:41

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### Calculus Related Rates Example Volume of Cone

by Allen Wolmer

A Youtube video on this topic. There may be short commercial content at the beginning.

Video duration:  11:13

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### Related Rates: Melting a Snowball

by Allen Wolmer

Calculus applet illustrating this topic. Security enabled Java required.

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### Related Rates Exercises

by Allen Wolmer

This set of exercises supports the following Standards of Mathematical Practice

• 1 Make sense of problems and persevere in solving them.
• 2 Reason abstractly and quantitatively.
• 4 Model with mathematics.
• 5 Use appropriate tools strategically.
• 6 Attend to precision.
• 7 Look for and make use of structure.
• 8 Look for and express regularity in repeated reasoning.
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### Rates of Change Per Unit Time Exercises

by Allen Wolmer

This set of exercises supports the following Standards of Mathematical Practice

• 1 Make sense of problems and persevere in solving them.
• 2 Reason abstractly and quantitatively.
• 4 Model with mathematics.
• 5 Use appropriate tools strategically.
• 6 Attend to precision.
• 7 Look for and make use of structure.
• 8 Look for and express regularity in repeated reasoning.
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### Related Rates Exercises

by Allen Wolmer

Mooculus Calculus Textbook Exercises, Sect 8.3 pp 143-145 (Ans p 252)

This set of exercises supports the following Standards of Mathematical Practice

• 1 Make sense of problems and persevere in solving them.
• 2 Reason abstractly and quantitatively.
• 3 Construct viable arguments and critique the reasoning of others.
• 5 Use appropriate tools strategically.
• 6 Attend to precision.
• 7 Look for and make use of structure.
• 8 Look for and express regularity in repeated reasoning.
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