if |x-3| < ε/7 and 0 < x ≤ 7 prove that |x^2 - 9| < ε
The Attempt at a Solution
So ths is what I did so far.
|x+3|*|x-3| < ε (factored out the |x^2 - 9|)
|x+3|*|x-3| < |x+3|* ε/7 < ε (used the fact that |x-3| < ε/7)
|x+3|* ε/7 *7 < ε*7|x-3| < ε/7*7 (multiplied both sides of the inequality by 7)
I suck at epsilon delta proofs and have no idea where to go from here.