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limits


I'm studying the definitions of limits: 
lim F(x)=L
x->a
I'm having trouble solving the proofs of the limits that have constants
I can solve it with the constant, but for the constant..
for example:

lim  2x^2=2
x->1

here's what I did:

|2x^2-2|<î	0<|x-1|<ë
2|x^2-1|<î
2|x-1||x+1|<î
2(k)|x-1|<î
|x-1|<î/2k	0<|x-1|<ë
ë=î/2k
this is as far as I can get... the books solves for 'k' and comes up with this
ë=min(î/6,1)
I don't see the connection.. help



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