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General Continuity Proof Question

  1. Nov 20, 2008 #1
    Ok, let's say I had [tex]3x^{2}-2x+1[/tex]
    I know we have lx-2l<[tex]\delta[/tex]
    Also l(x-2)(3x+4)l<[tex]\epsilon[/tex]
    My problem with these types of questions is dealing with the l3x+4l. I just don't really know what to do.
  2. jcsd
  3. Nov 20, 2008 #2


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    I'm not sure what you are looking for. However x~2 means that 3x+4~10. To be more precise |3x+4 - 10| < 3(delta).
  4. Nov 21, 2008 #3
    We can restrict δ > 0 to be as small as we want, so let's say δ ≤ 1. Then using |x - 2| < δ ≤ 1, show that |3x + 4| < 13, so that |(x - 2)(3x + 4)| < 13δ. In order for |(x - 2)(3x + 4)| to be less than ε, you can just pick any δ ≤ ε / 13; δ = max{1, ε / 13} does it.
    Last edited: Nov 21, 2008
  5. Nov 21, 2008 #4


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    It is generally a good idea to actually say what you mean! you say "these types of questions" without saying WHAT types of questions. Probably you mean "prove that 3x2- 2x+ 1 is continuous at x= 3". that's what adriank assumed an he gave a very nice explanation.
  6. Nov 26, 2008 #5
    Ok, I understand that. I just wasn't sure what to do when I got a quadratic because I understood these questions just fine otherwise.
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