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Problem

Find the limit, if it exists. If the limit does n…

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Problem 44 Medium Difficulty

Find the limit, if it exists. If the limit does not exist, explain why.

$ \displaystyle \lim_{x \to -2}\frac{2 - |x|}{2 + x} $


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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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Top Calculus 1 / AB Educators
Grace He
Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

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.

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Watch More Solved Questions in Chapter 2

Problem 1
Problem 2
Problem 3
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
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
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
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66

Video Transcript

This is problem number forty four of the Stuart Calculus. Eighth edition, section two point three. Final amid. If it exists, it's the limit does not exist. Explain why Here we have a limited six bridges. Negative too. Of the function to minus work. The absolute value backs divide where the quantity two plus sex. Okay, since this is a complete limit, not just a limit from the left or the right, we wantto determine first. Whether approach in a tutu makes this an indeterminate form or an undefined value. Two minus the absolutely of negative too is to minus two two plus native who? Zero. So we have a zero division here, divide by zero. Add some *** too. So we know that the value or the function is on to find a native to so we were unable to determine that it exists are at this point. Um, but we can still prove that ism it exists as long as the limited left negative two equals limit from the right. I'm negative too. On that the equal each other. So what we want to do is we want to first deal with this absolute value function, and we want to rewrite this Lim. I'm using what we know about the absolute value function of X. We know that when X is greater than zero or equal to zero, it's equal the function X. However, when X is negative, he also value is meant to change the sign and so dysfunctions represented by a negative X and for our interests since the limit of expertise and negative too. This is on ly in this region. So we will not be considering the absolute value function too. Take this form because we are only concerned with the X approaches negative to region. So we will substitute dysfunction with negative X instead. So rewriting this limit as experts needed to two minus native X or plus X divided by two plus X Now notice that I didn't write experts in ecstasy from the left or expert unit two from the right because both of those give you the same results right since we're pushing native to which is a value in this region. So the function looks the same, whether it's from the left or the right. As we can see, we can cancel these too, and this simplifies to one And if we take the Limited's experts think, too, of this constant value of one. Her answer for the limit is one again keeping in mind that this is true for both. Pushing is equal to negative to pushing that from the left and from the right. And since those Walter True and exist and they both equal one, then this limit from the beginning also equals one, and that is our final answer.

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Related Topics

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Top Calculus 1 / AB Educators
Grace He

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Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

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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