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Thread: [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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    $\displaystyle \lim_{x \to 3} 3x - 1 = 8$

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

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

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