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Unformatted text preview: Student Name: An Introduction to Limits and Derivatives (Part 1) (based on the project contributed by John Quintanilla) The purpose of this project is to give you an introduction to the two of the main concepts in calculus: limits and derivatives . Problem: A car at an intersection sits at a stop light. Once the light turns green, it accelerates away from the intersection. Assume that t seconds after the light turns green, the car is a distance of f ( t ) = t 3 meters away from the intersection. Graph the distance from the intersection as a function of time: f ( t ) = t 3 . t 1 2 3 4 5 6 f ( t ) = t 3 Let’s now try to figure out how fast the car is moving after 2 seconds. Notice that we can’t merely divide the distance by the time because the velocity of the car is changing with time. However, we can estimate the velocity after t = 2 seconds by dividing the distance it travels between 2 and 3 seconds by the time elapsed between 2 and 3 seconds: Average velocity = f (3)- f (2) 3 s- 2 s...
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