I am trying to prove the limit of the following:
$\lim x \rightarrow 1 $ of $x^2+2x$ where the limit $L = 3$
This gives us $0<|x-1|<\delta$ and $|x^2+2x-3|<\epsilon$
First I factorize $f(x) \rightarrow$ $|(x+3)(x-1)|<\epsilon$
$\rightarrow |x+3||x-1|<\epsilon $
I recognize that I get a matching term $|x-1|$, however I have an uncontrolled term $|x+3|$.
If I assume $|x-1|<\delta$ and $\delta < 1$
Edit, made some progress;
I.e. making a restriction that $x$ can be a maximum distance of 1 away from $a$.
$|x-1| < 1$
Thus, $\epsilon/|x+3|$ is at its minimum when $|x+3|$ is at its maximum