Proving a limit L using formal definition of a limit when limit is 0

[sealpuncher]

I can't figure out how to prove that L is 0 using the formal definition with epsilon and delta. Here's the lim. lim (x^2 + 3x)
x->-3
I can instantly figure out that the limit is 0 but I am having trouble deciding how to go about the proof. The work I have right now: |(x^2 + 3x) - 0| < e .. so does that mean my delta is just going to be e and the ratio is just 1:1? I'm so lost...εε

 

[galactus]

\(\displaystyle \displaystyle\lim_{x\to -3}(x^{2}+3x)=0\)

Given \(\displaystyle \epsilon > 0\)

\(\displaystyle |(x^{2}+3x)-0|<\epsilon\)

\(\displaystyle |x(x+3)|<\epsilon\)

\(\displaystyle |x+3|<\frac{\epsilon}{|x|}\)

If we assume \(\displaystyle -4<x<-2\), then \(\displaystyle \delta=\frac{\epsilon}{4}\)