- #1

Dani4941

- 6

- 0

I need someone to look over this problem and tell me if it's good. Not just if it's right but if it's perfect. I always get the problem right then get minus points because I didn't explain it enough.

So here it is

Give an ε-δ proof of

lim x->a of ((3x²-3a²)/(x-a)) = 6a

Proof: Note |f(x) – a| = |f(x) – 6a| = | (3x²-3a²-6ax-6a²)/(x-a) | = | (3(x²-2ax+a²)/(x-a)) | = |3x-3a|

|3x-3a|<ε (get rid of 3 to make it smaller) |x-a|<ε when |x-a|<δ let δ=ε

Given ε>δ let δ=ε

0<|x-a|<δ then

|f(x) – a| = |3x-3a|<δ=ε

Therefore

lim x->a of ((3x²-3a²)/(x-a)) = 6a