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Homework Help: Calculus: epsilon K proof

  1. Sep 20, 2010 #1
    1. The problem statement, all variables and given/known data
    Use [tex]\epsilon[/tex] K proof to show:
    [tex] lim \left(\frac{n^2 + 2n + 1}{2n^2 + 3n + 2}\right) = \frac{1}{2} [/tex]


    2. Relevant equations
    Hint first show
    [tex] \left| \frac{n^2 + 2n + 1}{2n^2 + 3n + 2}-\frac{1}{2}\right| \leq \frac{1}{2n}, \hspace{0.5cm} n\epsilon N[/tex]



    3. The attempt at a solution
    See the pdf. Please let me know if my argument can be more thorough.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Sep 20, 2010 #2

    HallsofIvy

    User Avatar
    Science Advisor

    At one point you have
    [tex]\frac{1}{n(2n+1)}< \epsilon \doublearrow \frac{1}{2n}< \epsilon[/tex]
    What you should say is "Because
    [tex]\frac{1}{2(2n+1)}< \frac{1}{2n}[/tex]
    if
    [tex]\frac{1}{2n}< \epsilon[/tex]
    it will be true that
    [tex]\frac{1}{2(2n+1)}< \epsilon[/tex]
     
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