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Evaluate the limit and justify each step by indic…

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Problem 6 Easy Difficulty

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

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Related Topics

Limits

Derivatives

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RT

Rr T.

February 18, 2021

Why did you put answer as 28 in text?

ll

Lingyu L.

September 25, 2019

Top Calculus 1 / AB Educators
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Catherine Ross

Missouri State University

Kayleah Tsai

Harvey Mudd College

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University of Nottingham

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Lectures

Video Thumbnail

04:40

Limits - Intro

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.

Video Thumbnail

04:40

Derivatives - Intro

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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Watch More Solved Questions in Chapter 2

Problem 1
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Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
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Problem 35
Problem 36
Problem 37
Problem 38
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Problem 40
Problem 41
Problem 42
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Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
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Problem 60
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Video Transcript

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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Calculus: Early Transcendentals

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Related Topics

Limits

Derivatives

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Grace He

Numerade Educator

Catherine Ross

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Samuel Hannah

University of Nottingham

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

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.

Video Thumbnail

04:40

Derivatives - Intro

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.

Join Course
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