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Basic Limit Problem

  1. Sep 7, 2014 #1
    1. The problem statement, all variables and given/known data

    Estimate the instantaneous velocity of a particle with position function s(t) = 2t2−4t at t = 1 using the four intervals [0.9, 1], [0.99, 1], [1, 1.01], and [1, 1.1].

    2. The attempt at a solution

    At t=1, y = -2

    Slope of a line: a = (y2 - y1)/(x2 - x1)

    = (y2 + 2) / (x2 - 1)
    = (2t2−4t +2) / (x2 -1)

    At t = 0.9

    = (2(0.9)2−4(0.9) +2) / (0.9 -1)
    = -0.2


    At t = 0.99

    = (2(0.99)2−4(0.99) +2) / (0.99 -1)
    = -0.02

    At t = 1.01
    = (2(1.01)2−4(1.01) +2) / (1.01 -1)
    = 0.02

    At t = 1.1
    = (2(1.1)2−4(1.1) +2) / (1.1 -1)
    = 0.2


    From the graph of the parabola, it's pretty obvious that the equation of the tangent line is y= -2

    But, I don't know where I'm going wrong.
     
  2. jcsd
  3. Sep 7, 2014 #2

    ehild

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    Homework Helper
    Gold Member

    The independent variable is t instead of x. :smile:

    You need the instantaneous velocity , that is, the slope of the tangent line. What is the slope of the line y=-2? So what is the instantaneous velocity at t=1?

    ehild
     
  4. Sep 7, 2014 #3
    Woops. The slope is obviously zero.
     
    Last edited: Sep 7, 2014
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