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In this lecture we begin the actual study of calculus. We take a first look at modeling rates of change, and give an overview of the material of lectures 616 on the differential calculus.
Quick Question
What is the slope of this line?
Answer
Outline
Outline for Modeling Rates of Change
Textbook
Modeling Rates of Change
Today's Homework
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Quiz
Modeling Rates of Change Quiz
Examples

While skiing, Josh rides a chair lift moving at 3 miles per hour up a hill. After he has skied down the hill, his average velocity for the round trip is 5 miles per hour. How fast did he ski?

Fill in the missing numbers in a derived table.

A automobile testing organization runs cars around a speed track to test performance. One test involves running a car around a 1200meter track at high speed, and recording the individual lap times and the average speed for the entire test. On one occasion, the results are recorded, but are missing the final lap time. The first 4 laps show times of 37 seconds, 25 seconds, 29 seconds, 27 seconds, and the average speed for the test is recorded as 112 miles per hour. Show that even without knowing the final lap time, we can conclude an error has most likely been made in recording the results.
Applets
 Average Velocity
 Rate of Change
 Derived Function
Videos
 Traveling 60 miles in half an hour gets you a speeding ticket
 Derived tables for x^{2}
