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Order 5 of the following sentences so that they form a logical proof by contradiction of the statement:

$\displaystyle{\lim_{x \rightarrow 7} 7x+12 = 61}.$

Choose from these sentences:

Wrong 5
Therefore, $\displaystyle{\lim_{x \rightarrow 7} 7x+12 = 61}.$
Choose $\delta>0$ so that $\delta<\frac{\epsilon}{7}$ .
Ask the teacher for extra credit.
$|7x+12-61| \\ = 7 |x - 7| < 7 \frac{\epsilon}{7} = \epsilon$
Suppose $\delta>0$
Assume $|x-7|<\delta$
Wrong 4
Let $L \in \mathbb{R}$
Suppose $\epsilon>0$

Your Proof:

Choose from these sentences:

Wrong 5
Therefore, $\displaystyle{\lim_{x \rightarrow 7} 7x+12 = 61}.$
Choose $\delta>0$ so that $\delta<\frac{\epsilon}{7}$ .
Ask the teacher for extra credit.
$|7x+12-61| \\ = 7 |x - 7| < 7 \frac{\epsilon}{7} = \epsilon$
Suppose $\delta>0$
Assume $|x-7|<\delta$
Wrong 4
Let $L \in \mathbb{R}$
Suppose $\epsilon>0$

Your Proof: