# Modeling Rates of Change

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## Lecture Notes

#### Related Rates

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Section 1, Page 1 to page 2

Related rates description. Example problem using Hooke's law.

Instructor: Prof. Jason Starr
Prior Knowledge: The Chain Rule and Implicit Differentiation (sections 4 and 5 of lecture 4)

#### Method for Solving Related Rates Problems.

PDF
Section 2, Page 2 to page 4

Step-by-step guide to solving related rates problems. Worked examples involving a speeding driver and a point moving on the x-axis.

Instructor: Prof. Jason Starr
Prior Knowledge: Related Rates (section 1 of this lecture) and Implicit Differentiation (section 5 of lecture 4)

#### One Review Problem: Related Rates

PDF
Section 4, Page 5 to page 6

Related rates worked example.

Instructor: Prof. Jason Starr
Prior Knowledge: Related Rates (section 1 of lecture 11)

## Exam Questions

#### Related Rates

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Problem 1 (page 2)

Finding the rate at which a particle moving on the x-axis is moving away from a point on the y-axis.

Instructor: Prof. Jason Starr
Prior Knowledge: None

#### Related Rates with Polar Coordinates

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Problem 6 (page 1)

Finding the rate of change of a particle's distance from the y-axis as it moves around the unit circle.

Instructor: Prof. Jason Starr
Prior Knowledge: None

#### Related Rates

PDF
Problem 3.3 (page 2) to problem 3.4 (page 2)

Two problems which involve a melting icicle and a melting block of ice.

Instructor: Prof. Jason Starr
Prior Knowledge: None

#### Related Rates

PDF
Problem 8 (page 1)

Finding the rate of change of the radius of a balloon with decreasing volume.

Instructor: Prof. David Jerison
Prior Knowledge: None

PDF
Problem 10 (page 1)

Finding the time for a substance to decay to one-fourth its original amount, and the rate at which it is decaying at this time.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Related Rates

PDF
Problem 5 (page 1) to problem 6 (page 1)

Two questions involving the rate of change of the angle of a falling tree and the rate of change of the water level in a cone.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Related Rates: Searchlight

PDF
Problem 4 (page 1)

Finding the rate at which a prisoner needs to run to stay ahead of a searchlight

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Viewing Angle for a Launching Rocket

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Problem 4 (page 1)

Finding the rate of change of the angle at which a person is watching a rocket ten seconds after it takes off

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Related Rates: Christmas Tree

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Problem 5 (page 1)

Finding the rate at which the shadow of a falling Christmas tree is lengthening.

Instructor: Prof. David Jerison
Prior Knowledge: None