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Math Help - [SOLVED] Cauchy epsilondelta proof

  1. #1
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    [SOLVED] Cauchy epsilondelta proof

    Can anyone check if this is going to turn out right


    Use cauchy e-6 proof to show that lim(3x-1)=8


    http://www.ocf.berkeley.edu/~yosenl/...ilon-delta.pdf

    what i did was exactly what they did put switched out the numbers

    i really only need this 1 problem because im doing HS calculus and the teacher assured us that this would not re occur in the course.
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  2. #2
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    \lim_{x \to 3} 3x - 1 = 8

    Going by definition:
    \forall \epsilon > 0, \ \exists \delta > 0 such that whenever 0 < {\color{red}|x - 3|} < \delta it follows that \left| 3x - 1 \ - 8 \right| < \epsilon

    Looking at:
    \begin{array}{rcl}\left| 3x - 1 \ - 8 \right| & < & \epsilon \\ \mid 3x - 9 \mid & < & \epsilon \\ 3 {\color{red}|x-3|} & < & \epsilon \\ & \vdots &\end{array}

    You know |x-3| < \delta and we have that final line. What should you set \delta equal to in terms of \epsilon?
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  3. #3
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    Is it e/3
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