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Problem

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

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Problem 26 Easy Difficulty

Find the limit or show that it does not exist.

$ \displaystyle \lim_{x \to \infty}\frac{x + 3x^2}{4x - 1} $


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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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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
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Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
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

This is a problem. Number 26 of the Super Calculus eighth edition section 2.6. Find the limit or show that it does not exist. The limit as experts is infinity X plus three X squared, divided by quantity four X minus one. And what we're going to, uh, look to use is that limit as experts. Infinity of a. An expression of the form, one of our extra R where R is a rational value. Graded zero. Islam is equal to zero. If we were to help produced this limit into forms of this definition to our advantage, it will be divided by X in the numerator and the denominator. Our first term is X or X is one plus three x squared over excess three X and the denominator. We will get for extra by excess for minus one over X is one or X. Now we use our properties limits, which allow us to take the LTD each of these terms individually. And then we used the definition and we know that this term approaches zero as X approaches infinity a mistake. Islam. It is the same as the original experts infinity. And so there's one of Rex term approach Jazeera. As exporters affinity the numerator we can see approaches three times infinity. So the numerator will actually be approaching infinity in this case, since it gets bigger without bound numerator, denominator remains at 40 approximately. But this is the same as positive. Infinity, as for, is much smaller than infinity. So what we say is that this limit does exist and it's an infinite limit equal to infinity. Positive infinity.

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Related Topics

Limits

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Top Calculus 1 / AB Educators
Catherine Ross

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Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Kristen Karbon

University of Michigan - Ann Arbor

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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