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Homework Help: Limit of cos x as x approaches 1 formal

  1. Sep 16, 2009 #1
    1. The problem statement, all variables and given/known data

    The limit of Cos X as x approaches one using the formal definition.
    Given epsilon values of .1, .001, .00001

    2. Relevant equations

    3. The attempt at a solution

    Spent all period in physics calc trying to solve this using the formal definition.
    Since there is no way to manipulate abs(cosx-.5403)<epsilon
    I proceeded to make my delta = the epsilon values and plug into the equation.
    None of the answers were working correctly. Any help would be greatly appreciated because i have a feeling that im missing something here.
  2. jcsd
  3. Sep 16, 2009 #2


    Staff: Mentor

    It appears you want to find the individual values of delta when epsilon is .1, .001, and .00001.

    Set up your inequality for each of these values.
    For epsilon = .1

    |cos x - 0.5403023| < .1
    <==> -.1 < cos x - 0.5403023 < .1
    Continue in this vein until you have cos x between two values, and then use cos-1 to get an inequality in x. At that point you should have a good idea what to use for delta.

    Do the same for the other two values of epsilon.
  4. Sep 16, 2009 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hint: You might find this identity useful:

    [tex]\cos{a} - \cos{b} = -2 \sin \frac {a+b} 2 \sin \frac {a-b} 2[/tex]
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