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#1 2014-09-11 02:01:47
- mrpace
- Member
- Registered: 2012-08-16
- Posts: 88
Prove this limit
show, using the formal definition of a limit, that:
lim
x^2=4
x -> 2
I'm getting to a point where I have |x+2||x-2| < E
But I don't know where to go from there. Help is much appreciated.
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#2 2014-09-11 02:10:57
Re: Prove this limit
There is no need to factor it. You are confusing yourself by factoring it
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#3 2014-09-11 03:01:03
- mrpace
- Member
- Registered: 2012-08-16
- Posts: 88
Re: Prove this limit
There is no need to factor it. You are confusing yourself by factoring it
Really? I'm trying with it not factored and not having any luck.. can you help?
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#4 2014-09-11 21:12:10
- Olinguito
- Member
- Registered: 2014-08-12
- Posts: 649
Re: Prove this limit
You’re on the right track, but sometimes you just need to be a little creative. By the triangle inequality
[list=*]
[*]
[/list]
Hence
so you can choose such that , i.e. (note that ).Last edited by Olinguito (2014-09-11 21:17:25)
Bassaricyon neblina
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