Originally Posted by

**Jhevon** i assume you know the definition you should be working with. i will do 95% of the problem for you and leave you to finish of

we want $\displaystyle |f(x) - 4| < \epsilon$

$\displaystyle \Rightarrow |6 + x - 3x^3 - 4| < \epsilon$

$\displaystyle \Rightarrow |2 + x - 3x^3| < \epsilon$

$\displaystyle \Rightarrow |3x^3 - x - 2| < \epsilon$

$\displaystyle \Rightarrow |3x^2 + 3x + 2||x - 1| < \epsilon$

Now, when $\displaystyle x$ is "near" 1, we have:

$\displaystyle 8|x - 1| < \epsilon$

$\displaystyle \Rightarrow |x - 1| < \frac {\epsilon}8$

now finish up