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Calc I 'graphical analysis' question

  1. Jan 3, 2009 #1

    This is a question from Larson's calculus that I never was quite sure what exactly I'm supposed to do.

    Do I graph -.001 < ((x^2 - 4)/ (x - 2) - 4) < .001

    with something like when x <.001 ((x^2 - 4)/ (x - 2) - 4) and when x > .001 ((x^2 - 4)/ (x - 2) - 4) but I just get "undefined variable" errors (it does begin to graph it, though).

    Do I solve abs(((x^2 - 4)/ (x - 2)) - 4) and then graph it?

    Is this problem tyring to show that the delta values will be between the upper and lower bounds of | f(x) -L | < epsilon.

    I'm not sure this a problem compatible with my calculator.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jan 4, 2009 #2


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    I don't know your "graphing facility" so I don't know what "undefined variables" you are getting but I would graph
    1) y= (x^2- 4)/(x- 2)
    2) y= 4- 0.01 and
    3) y= 4+ 0.01

    If your facility actually begins to graph it and then gives an error message, it may actually be a "divide by 0" problem at x= 2. Try graphing the three functions above with a window x= -1 to x= 2 and then again with x= 2 to x= 3
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