# Thread: Prove using epsilon - delta definition of a limit?

1. ## Prove using epsilon - delta definition of a limit?

How can I prove lim x->1 (x^2 + 4x) = 5 and lim x->2 (1/x^2) = 1/4 using the epsilon - delta definition of a limit?

2. For example:

$\displaystyle |x^2+4x-5|<\epsilon \Leftrightarrow \ldots \Leftrightarrow |x-1||x+5|<\epsilon$

Now, use that $\displaystyle |x+5|$ is bounded on $\displaystyle [0,2]$ .

Fernando Revilla

3. why bounded on [0,2]? How did you get these intervals? And why |x + 5|? Why not x-1?

4. Originally Posted by colerelm1
why bounded on [0,2]? How did you get these intervals? And why |x + 5|? Why not x-1?
Because the limit involves $\displaystyle x\to 1$, the definition will include $\displaystyle |x-1|<\delta$ and not $\displaystyle |x+5|$.
Thus you need to bound the other factor.