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Problem

Find the limit or show that it does not exist. …

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Problem 15 Easy Difficulty

Find the limit or show that it does not exist.

$ \displaystyle \lim_{x \to \infty}\frac{3x - 2}{2x + 1} $


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02:39

Daniel Jaimes

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Related Topics

Limits

Derivatives

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Top Calculus 1 / AB Educators
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Catherine Ross

Missouri State University

Heather Zimmers

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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
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Problem 5
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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
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Problem 24
Problem 25
Problem 26
Problem 27
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Problem 38
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Problem 61
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Problem 63
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Problem 68
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Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81

Video Transcript

All right. We've got this limit problem. Um We want to find this limit or show that it does not exist. A couple different ways of doing this. Some people like to do uh low petals rule because it's fast. Um I don't like that because limits have to exist before derivatives do. Um Some people like to think about and behavior that's not terrible. Um Actually, if X is growing, I just like to stop it from growing because I don't know what big really big over really big is and that's what we have right now. Um So I'm just gonna make it small. I'm going to divide top and bottom by X. So three x divided by X. three. Um And now I have two times one over X. And then two X divided by X. Two. And then I have one times one over X. And then the only theorem I need for ex growing is as X gets big one over X gets small. You agree with that one divided by a really huge Number is always going to be zero. So then I can plug that theorem into these limits. Right? Um limits can add subtract multiply as long as everything exists. So I have three minus two times zero. Because that thing is going to be zero. When X is big divided by two plus zero. So I'm going to get three minus two times zero divided by two plus zero is 3/2. I think that's the cleanest way to think about this

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Related Topics

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Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Heather Zimmers

Oregon 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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