exploration1

# exploration1 - Exploration 1 Instantaneous Rate of Change...

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The diagram shows a door with an automatic closer. At time t = 0 seconds someone pushes the door. It swings open, slows down, stops, starts closing, then slams shut at time t = 7 seconds. As the door is in motion the number of degrees, d, it is from its closed position depends on t. 1. Sketch a reasonable graph of d versus t. 2. Suppose that d is given by the equation d = 200t 2 - t . Plot this graph on your calculator. Sketch the results here. 3. Make a table of values of d for each second from t = 0 through t = 10. Round to the nearest 0.1˚. 4. At time t = 1 second, does the door appear to be opening or closing? How do you tell? 5. What is the average rate at which the door is moving for the time interval [1, 1.1]? Based on your answer, does the door seem to be opening or closing at time t = 1? Explain. 6. Find an estimate of the instantaneous rate at which the door is moving at time t = 1 second. Show how you get your answer. 7. In calculus you will learn by four methods: • algebraically, • numerically, • graphically, • verbally (talking and writing).

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exploration1 - Exploration 1 Instantaneous Rate of Change...

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