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University of California, Berkeley

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Problem 56

Using the $\varepsilon$ -\delta Definition of Limit In Exercises $45-56$ , find the limit $L$ . Then use the $\varepsilon-\delta$ definition to prove that the limit is $L$ .

$$\lim _{x \rightarrow-4}\left(x^{2}+4 x\right)$$

Answer

$$\min \{|-2+\sqrt{4-\epsilon}|,|-2-\sqrt{4-\epsilon}|\}$$

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## Discussion

## Video Transcript

Okay, so we have the limit as extra searches for Alexis too. What is that? That's four plus two, which is six now. Have our value of our function exposed to minus six. This is he put it after the value of X minus four. But we know that the limit as ex opposes for our function for each Absalon greater than Bill. There's this Delta greeted Bill. Such that, um after ah, value of our function might have six is an excellent whenever narrows Dustin exploited for us. So for any given absalon grated and so we can choose Delta equal to Absalon. Then you have that after a bout of excellent for us in Delta, which is equal to act alone. This implies that our function we're next physical too export to money six, which is equal to x amount of support. You have been excellent. So our limits is equal to six, which means yeah. So this spell to decode that one

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