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limits

• To: mathgroup at smc.vnet.net
• Subject: [mg5281] limits
• From: ryanjone at stinger.redshift.com (Ryan Jones)
• Date: Mon, 18 Nov 1996 02:30:33 -0500
• Organization: Redshift Online Service
• Sender: owner-wri-mathgroup at wolfram.com

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