# Homework Help: Calculus: epsilon K proof

1. Sep 20, 2010

### Winzer

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

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

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:

• ###### Homework3.pdf
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2. Sep 20, 2010

### HallsofIvy

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
$$\frac{1}{2(2n+1)}< \epsilon$$