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Math Help - Variety of Calculus questions

  1. #1
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    Left and Right hand sums.

    t (s) 0 12 24 36 48 60
    v (ft/s) 32 28 24 22 24 28
    Readings at 12 second intervals. Estimate distance traveled Deltax= 12

    1. estimate distance using the velocities in the beginning of the time intervals:

    =156 = 12(28+24+22+24+0)=L6 This is correct



    2. give another estimate at the end of the time intervals.

    I did 12(32+28+24+22+24+28) = 1896 =R6 Which is wrong


    PART B)

    Are your estimates in parts (a) and (b) upper and lower estimates? Explain.

    a (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
    b (a) is a lower estimate and (b) is an upper estimate since v is an increasing function of t.
    c. (a) and (b) are neither lower nor upper estimates since v is neither an increasing nor decreasing function of t

    I chose b but it's wrong. But I believe it is choice c since the intervals are an irregular curve
    Last edited by Steelers72; February 7th 2013 at 02:23 PM.
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  2. #2
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    Re: Variety of Calculus questions

    Hey Steelers72.

    I am also inclined to go with c) as well for the answer.
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  3. #3
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    Re: Variety of Calculus questions

    Yes, (c) is correct: v decreases from 24 to 36 and increases from 36 to 48.

    For the first part of the problem, I get:
    using velocity at beginning of interval: 12(32+28+24+22+24) = 1560
    using velocity at end of interval: 12(28+24+22+24+28) = 1512

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  4. #4
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    Re: Variety of Calculus questions

    Thank you for your replies! Im confused with the end of interval. Why would 32 not be included? I was thinking not to include the 60s and 28 ft/s since it's at the end(?) You're right, but could you explain why 32 is left out? thanks again!!
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  5. #5
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    Re: Variety of Calculus questions

    Oh wow, never mind! I answered my own question.

    For left hand sums, you leave out the right-most measurement and for right hand sums you leave out the left-most measurement right?
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  6. #6
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    Re: Variety of Calculus questions

    That's correct.

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