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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} $

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03:14

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Limits

Derivatives

Rr T.

February 18, 2021

Why did you put answer as 28 in text?

Lingyu L.

September 25, 2019

Missouri State University

Harvey Mudd College

University of Nottingham

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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Evaluate the limit and jus…

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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.

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