Limits using Epsilon Delta definition $$\lim_{x \to 3} x^{3}=27 $$
$$ 0<|x-3|<\delta$$ 
$$|x-3||x^{2}+3x+9|< \varepsilon$$
My teacher said that delta must be in the interval [0,3] but I don't think it's correct. 
What is the correct approach to solve this kind of questions?
Thanks in advance.

take$ \delta = min(1,\frac{\varepsilon}{37})$
then $|x-3||x^{2}+3x+9|< 37|x-3| < \epsilon $
