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Math Help - Simple limit problem

  1. #1
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    Simple limit problem

    For the function f(x) = 2√(2x-2), find delta such that |2√(2x-2) - 4| < 0.5 whenever |x - 3| < delta.

    (Determine how close x must be to 3 to ensure that f(x) is within 0.5 of 4)

    Any insight onto this problem? I don't know where to start really
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Intrusion View Post
    For the function f(x) = 2√(2x-2), find delta such that |2√(2x-2) - 4| < 0.5 whenever |x - 3| < delta.

    (Determine how close x must be to 3 to ensure that f(x) is within 0.5 of 4)

    Any insight onto this problem? I don't know where to start really
    What have you tried?
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  3. #3
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    2√(2x-2) < 3.5
    √(2x-2) = 3.5/2
    2x -2 = (3.5/2)^2
    x = 2.53125

    2√(2x-2) < 4.5
    √(2x-2) = 4.5/2
    2x -2 = (3.5/2)^2
    x = 3.53125


    3.53125 - 3 = .53125
    3 - 2.53125 = .46875

    So .46875 is delta.
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