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**iLikeMaths** prove using the $\displaystyle \epsilon , \delta$ definition of continuity that $\displaystyle f(x) = x^3 - 2x^2 + 1$ is continuous at $\displaystyle x=3$

this is the start of my solution, however i need help complting it

$\displaystyle f(x) = x^3 -2x^2 +1$

$\displaystyle c=3$

$\displaystyle f(c)= 27-18+1 = 10$

for each positive number $\displaystyle \epsilon$

$\displaystyle |f(x) -f(c)| < \epsilon$ for all $\displaystyle x $ satisfying $\displaystyle |x-c|<\delta$

and then i get

$\displaystyle |x-3||x^2 + x +3|<\epsilon$ for all $\displaystyle |x-3|<\delta$

so my question is what is the value of$\displaystyle \delta$, can i just use any random number or does it have to be specific?