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?
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