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Math Help - [SOLVED] limits word problem

  1. #1
    Member sinewave85's Avatar
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    [SOLVED] limits word problem

    This problem is from a lesson on informal computation of limits:

    Tom and Sue are driving along a straight, level road in a car whose speedomenter needle is broken but that has a trip odometer that can measure the distance traveled from an arbitrary point in tenths of a mile. At 2:50 pm, Tom says he would like to know how fast they are traveling at 3:00 pm, so Sue takes down the odometer readings listed in the table, makes a few calculations, and anounces the desired velocity. What is her result?

    time 2:50 2:55 2:59 3:00 3:01 3:06
    odometer reading 33.9 38.2 41.5 42.4 43.2 44.9


    My work:

    interval length 10 5 1 0 1 3 6
    interval distance 8.5 4.2 0.9 x 0.8 2.5 5
    average velocity 0.85 0.84 0.9 x 0.8 0.83 0.83

    The velocities in the table don't seem to converge to any specific value. If the third odometer reading was 41.6 , the velocities would converge to 0.8, but I have checked and rechecked, and the book says 41.5. How do I find the velocity?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sinewave85 View Post
    This problem is from a lesson on informal computation of limits:

    Tom and Sue are driving along a straight, level road in a car whose speedomenter needle is broken but that has a trip odometer that can measure the distance traveled from an arbitrary point in tenths of a mile. At 2:50 pm, Tom says he would like to know how fast they are traveling at 3:00 pm, so Sue takes down the odometer readings listed in the table, makes a few calculations, and anounces the desired velocity. What is her result?

    time 2:50 2:55 2:59 3:00 3:01 3:06
    odometer reading 33.9 38.2 41.5 42.4 43.2 44.9


    My work:

    interval length 10 5 1 0 1 3 6
    interval distance 8.5 4.2 0.9 x 0.8 2.5 5
    average velocity 0.85 0.84 0.9 x 0.8 0.83 0.83

    The velocities in the table don't seem to converge to any specific value. If the third odometer reading was 41.6 , the velocities would converge to 0.8, but I have checked and rechecked, and the book says 41.5. How do I find the velocity?
    Look at the average speed between 2:50 and 3:06, then that between 2:55 and 3:06, then between 2:59 and 3:06, then between 2:59 and 3:01.

    (they wont converge, the speed at 3:00 is the maximum)

    RonL
    Last edited by CaptainBlack; June 4th 2008 at 12:12 AM.
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