How to use epsilon K proof to show a limit using Calculus?

Winzer
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Homework Statement


Use \epsilon K proof to show:
lim \left(\frac{n^2 + 2n + 1}{2n^2 + 3n + 2}\right) = \frac{1}{2}


Homework Equations


Hint first show
\left| \frac{n^2 + 2n + 1}{2n^2 + 3n + 2}-\frac{1}{2}\right| \leq \frac{1}{2n}, \hspace{0.5cm} n\epsilon N



The Attempt at a Solution


See the pdf. Please let me know if my argument can be more thorough.
 

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