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Math Help - Limits

  1. #1
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    Limits

    This is probably pretty easy and I'm just over-thinking it, but I have no clue what to do for this problem.

    If \lim_{x \to3} (3x-2)=7, find S such that |(3x-2)-7|<0.003 whenever 0<|x-3|<S.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by summermagic View Post
    This is probably pretty easy and I'm just over-thinking it, but I have no clue what to do for this problem.

    If \lim_{x \to3} (3x-2)=7, find S such that |(3x-2)-7|<0.003 whenever 0<|x-3|<S.
    Note that \left|(3x-2)-7\right|=\left|3x-9\right|=3{\color{red}\left|x-3\right|}<0.003 whenever 0<{\color{red}\left|x-3\right|}<S.

    With this, what is S?
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  3. #3
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    I think S is just a symbol for whatever that number is that is supposed to fit in the last equation.

    But so therefore, S = 0.001?
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by summermagic View Post
    But so therefore, S = 0.001?
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