delta epsilon relationship

Question

In formally proving that lim _{x → 3} (x^3 - 3x^2 +4x) = 12 , let ε> 0 be arbitrary . Choose δ = min(ε/m , 1) 

Determine m. 

I cant figure out what to do after factorizing. 

I have the following:

                 (|X-3||x^2+4|) < ε and |x-3|<δ

 

now for a restriction |x-3|<1      -1<x-3<1 

this is as far as i got. not sure what to do about the |x^2+4|  could i tried to  factor (x+2)(x+2)  but this doesn't lead me anywhere either. 

Answer 1

Since the function of which you seek the limit is a polynomial, all of which are continuous, lim (as x→a) f(x) = f(a) for any a ε ℜ.