# Thread: [SOLVED] Cauchy epsilondelta proof

1. ## [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.

2. $\displaystyle \lim_{x \to 3} 3x - 1 = 8$

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 $\displaystyle \epsilon$?

3. Is it e/3