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Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).

$ \displaystyle \lim_{u \to -2}\sqrt{u^4 + 3u + 6} $

$28$

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Lingyu L.

September 25, 2019

Rr T.

February 18, 2021

Why did you put answer as 28 in text?

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And this problem were asked to evaluate this limit and list the limit laws as we work through the problem. So we're given the limit as you approach is -2 of the square root. The view of the 4th was three U plus six. All right. So by the limit law that some of the limit of the sums of the summer limits. In other words, limit is X approaches a of F of X plus gm X Pink bowls the limit as X approaches a F of X plus limit as X approaches a G F X very clean that up just a little bit and has the limit as X approaches a of the square root of F of X is the square root of the limit. As X approaches a F of X By these two laws. Mhm. Mhm. Then we have the square root Of the limit as X approaches minus to a view to the 4th. Was the limit as not X should be a right. I mean you should be you You approach is -2 of three. You plus the limit As you approach is -2 of six. Okay, so as polynomial is a continuous function, then We have the square root of -2. The fourth plus three times minus you. Which by the way is the law that limit as X approaches a of C. F of X or C As some constant number. Is that constant number times the limit as X approaches a. Of fx. So that gives us that uh not minus you. Right, would be Oh no, okay. Ah This is not my issue. This is minus two right here. And then limit law at the limit as X approaches a. See some constant. It's just that constant. So that's plus six. So that gives us the square root of well 2 to the 4th. That's that's four square. That's 16 minus six plus six, which then means we have the squirt of 16, which is four. Therefore, answer is for for this limit.

Oklahoma State University