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Homework Help: Finding the best interval of solutions for N (using epsilon)

  1. Oct 9, 2011 #1
    The problem is:

    lim as x→- ∞ (-5x/x-2)=-5

    And I have to find the best interval of solutions for N

    Relevant equations:
    if x>N then |(-5x/x-2)-(-5)|<ε

    My attempt:

    |(-5x/x-2) - (-5)|<ε


    x-2< 10/ε

    as x→-∞ we can assume that x-2<0


    x< (10/ε)+2

    therefore, the interval should be NE [(10/ε) +2, -∞)

    however, the answer says that it should be -2 not +2. I don't know what I am doing wrong, if anyone can help that would be great! Thanks!
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 9, 2011 #2


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    Science Advisor
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    Gold Member

    Of course, you should write that fraction as -5x /(x-2) here. Use parentheses!

    At this step you have 10/|x-2| < ε

    No. You should have |x-2| > 10/ε. You need absolute value signs and the inequality is reversed.

    If x - 2 < 0, what is |x-2|?
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